This is a great theme worth exploring. By no means was the alliance between Liberals and SDs a natural event, it was made natural by the leadership of David Steel and Roy Jenkins. I think for this separation and contest (at some level) to work you would need to remove David Steel from the leadership of the Liberal Party. I think the most natural POD here would be for Boy David to lose the leadership contest to John Pardoe in '75, though that means no Lib-Lab Pact and that's a story/timeline in it of itself as well. John Pardoe regarded David Steel's lack of pressure on Roy Jenkins to join the Liberal Party as close to treason. If we allow for Pardoe to become Leader of the Liberals and have him survive the '79 general election with a seat (maybe he does not go out of his way to fight to save Thrope's seat and appear at Thorpe's rally in person all common sense to contrary). Pardoe would pressure Roy to join the Liberals, but Roy was a schismatic, not an aisle crosser. However, Pardoe could easily get David Marquand to join (Marquand volunteered to join the Liberals in OTL and was talked out of it by David Steel, who warned such an act would only bring in two to three more MPs, while a separate party could cause a bigger revolt). Marquand was seen at the weather-vane of Roy Jenkins and that would fuel rumors (or is it rumours) that Roy would soon bolt as well. But I do not see Roy bolting, just dallying with it and then going to SDP.
All this would mean we would not have a natural leader to the Gang of Four, but I'd hesitate to crown David Owen. Shirley Williams was not ready for the burden of leadership (as I recounted in my timeline below - thumb up, cheap pop!). But Dr. David Owen was more or less her choice for leadership of SDP in juxtaposition to Roy Jenkins. In '82, the good doctor was seen as left of Roy, at least by Shirley. Alarmed by Roy's centrist tendencies and love of Liberals, Shirley backed David to challenge him to take the party leftwards. With the threat of Roy leadership neutralized, Shirley might well turn to the Ringo of the Gang of Four - Bill Rodgers. David Owen was not a natural choice for leadership in the eyes of the rank and file and his fellow MPs until after the Falklands War, when his genuine nationalism and support for the War impressed people. But that was once again due to being contrasted to a rather hapless Roy Jenkins, whose performance in the Commons in '82 and '83 was absolutely awful. Roy was unsuited to be a leader of a small party in the House. David Owen got a lot of press because while Roy struggled, he seemed to be on firm ground. But all of this is post-Falklands and in '82. In '81, post Wembley Labour conference disaster, the Gang of Three with Roy lurking only in the shadows would not be in a hurry to nominate a strong leader to speak for them all, they would try to push for a consensus troika. Once that would be unfeasible, due to how modern politics work, I can see Shirley pushing for Bill Rodgers as much as David Owen. Bill had stronger Cabinet credentials, had connections to more Labour politicians and although he did not love Gaitskell with the passion that Roy had for the man, he was a Gaitskellite through and through and was a Social Democrat from the Social Democratic wing of the Labour Party. David Owen was a parvenu. He joined the Party late in his life, had no history of activism prior to joining and was the last man of the Gang of Three to leave the Party, and was pushed into it by being heckled at the Labour conference. Yes, he was charismatic and yes with exposure of TV he could win the vote among the SDP members, but it was no sure thing. Bill Rodgers, motivated, and freed from the shadow of his politically bigger brother Roy could have been made leader of the SDP. Paradoxically, it was the shadow of Roy that drove David Owen. Without Roy being on the other side, David might not fight as hard to slay his opponent. Oh he'd still have went off into his tent to sulk had he lost (as he did Roy in OTL) and he would have been absolutely nasty to deal with for months afterwards, but I can see Bill beating David for leadership.
So, with John Pardoe on the Liberal side, with Boy David as a vocal member of his Party, but shut out of leadership and strategy, the Liberals would be less likely to make a deal with any other Party, SDP or otherwise. John Pardoe favored broad front at sending out as many Liberals to contest as many seats as possible and parachute dropping activists into wastelands and building up Liberal vote there rather than wait for it to spring up on its own. He would not be as ready to agree to let SDP contest 311 seats in the next general. He would negotiate hard.
Bill Rodgers or David Owen would not be in a position to play friends to Liberal in seat selection as well. Here it is hard to say who would be a bigger hardliner. In OTL, Bill Rodgers nearly sunk the alliance electoral pact by going to the press about the problems of negotiating with Liberals. David Owen is... David Owen. Negotiating was not in his forte, at least not with anyone who was male and arguing with him as his equal or near-equal. Dr. Owen could take orders (he worked wonderfully with Barbara Castle as her subordinate), and Dr. Owen gave orders. Dr. Owen was not collegiate. So without a formal electoral pact, SDP and Liberals would either embark on mutual self-destruction or an informal pact.
John Pardoe would not guarantee the SDP that no Liberal would run in any seat currently held by an SDP MP defector from Labour, but he could step back and allow SDP to run against vulnerable Labour seats where Liberals were not doing well, in exchange for SDP agreeing not to run against vulnerable Tory seats. It is hard to remember or grasp, but conventional wisdom held that SDP would act as Labour Party Mark II at one point and take over for Labour in Labour held areas. It took a couple of by-elections and one general to destroy that wisdom and realize SDP was drawing centrist voters from disaffected Tories in the same proportion as Liberals and was drawing largely the same small amount of disaffected of Labour voters as the Liberals. So all of these informal negotiations would take place before such discoveries are really made. It would be a rough and tumble not quite quid pro quo for seats and it would be messy and leave bad feeling on both sides.
There would no be SDP Glasgow-Hillshead in such a timeline. Nor SDP Warrington. Both of those relied on Liberal activists to work side by side with SDP "political virgins." SDP provided the troops, but it was experienced local Liberal canvassers who were showing them how to fight third party by-election in both cases. There would still be victories. And Shirley and Roy would make it into the House, just in other places. A non-aligned Roy could even be tempted to take over a Tory seat in Maidstone, whose Tory MP John Wells in OTL suggested Roy take the seat because John Wells is a very curious human being.
Ultimately, in the '83 general election of this timeline, with SDP contesting about 100 seats (if led by Bill Rodgers), would suffer no worse than they did in OTL. Maybe they would do a bit better, as they could focus their energies on a small set of seats. There would be less bloodshed over who would lead the Alliance (in the dark book of odd political backstabbing, Steel's attempted palace coup to oust Jenkins deserves a chapter by itself). Yes there would be some confusion on the part of the voters as to why people who agree on most things would form two different Parties and fight each other (in some seats) and the feel good factor of The Alliance working together would be lost, but in its place would be a more traditional political fist fight that most people could understand.
Liberals in '83 would do better than in OTL, in the sense they'd win more seats than in OTL, but they would lose deposits in a lot more seats in OTL and John Pardoe would not survive the subsequent purge due to the financial issues and the demoralizing effect of so many loses across the board. The broad front strategy would be retired and we might see Boy David take the throne. But by this point, Liberals and SDP would be separate journeys due to their respective leaders.