Look at it this way, in June 1940, Germany and Italy have conquered Albania, Belgium, Czechoslovakia, Denmark, the Netherlands, Norway, Poland and a bit more than half of France. Hungary, Romania, Spain, the USSR, and Yugoslavia are Axis-friendly neutrals.
That's a lot of economic power if they have a chance to integrate it. Hitler has also repeatedly broken treaties he signed, so there really isn't any basis for trust - Hitler currently has war, and as soon as he doesn't comply with his treaty obligations he'll get war again. Additionally, Japan's FIC pressure threatens to unhinge the entire premise of British defence in the Far East.
If the Axis are allowed to settle down to put their armies into their factories and start churning out warships, in two years they will be able to dispute the Med and the North Sea. Britain can't get into the Baltic to destroy the KM at anchor, but also can't take the whole RN into the Med to curbstomp the RM or over to Singapore to curbstomp the IJN (assuming that the autumn 1940 RN actually can curbstomp the IJN, which is another topic) until there is no KM in the Baltic, so giving Hitler and Mussolini time to take the money from their conquests and spend it on new battleships seems like a really bad idea.
So Britain needs any peace to be one that doesn't leave the Axis so victorious that they can come back for round two at a time of their choosing with enough force to take Blighty.
Getting Hitler to accept that kind of peace is the tricky bit. Obviously, given that Hitler's actual aim is to have a peaceful backyard when he does his drang nach osten, Britain has a stronger negotiating hand than it actually realises.
So, if they agree on German withdrawal from Norway, the Low Countries, Denmark, and France except Elsass-Lothringen, while retaining Poland. Britain might actually insist on A-L staying French, to be honest. Th
If the Italians haven't invaded British Somaliland yet, then they won't get it. If they have, then Britain will swap it back in exchange from withdrawing from Italian Libya.
Equally, if Japan hasn't invaded French Indochina yet, then they won't get it either. If they have, then they will withdraw, but the French will stop rail shipments to the Nationalist Chinese from Haiphong, until they've got a new colonial corps with some armor shipped over, at which point the sales of French surplus for American money will restart.
Note that there will be no Tizard mission, nor will Tube Alloys be shared with the USA. Some of the Vinson-Walsh naval expansions may not come to pass if the truce is fast enough (Germany needs to announce withdrawal from France, and Japan abandon its pressure on FIC, by mid-July 1940)
So basically this is Hitler gambling again, particularly that he'll be able to do again exactly what he did last time - drive east with mobile warfare, take Moscow, and force Soviet surrender before France can re-arm enough to break the Siegfried Line. He's the party with the biggest appetite for risk, and his judgement has been great so far.
Then there's a year of drama. Finland comes a plucky second in the Winter War, the Baltics cease to be, France and the Netherlands rearm tepidly, Japan stews with rage and tries to build carriers even faster.
Hitler points to Anglo-French arms manufacture as the rationale for the German ramp up in early 1941, Stalin may or may not believe him.
Barbarossa goes off on schedule and France ramps up its war production away from a colonial campaign in Vietnam towards a rematch with Germany.
Now, the key bits are that the Luftwaffe in particular isn't punished but the BoB, and some resources used to replace its losses can instead be directed to increasing the mechanisation of the Heer.
With no Western Desert campaign, Britain has quite a few tanks to put into a new BEF and quite a few planes to become a new AASF. It also has quite a few older planes to either ship out East or give to the French... to ship out East.
A key question is what Japan does. It can't stick to the OTL timetable without FIC from which to transit Thailand to attack Malaya. Hitler may ask Japan to try a Franco-Japanese War in June 1941, but that might well be intercepted by Sorge before his execution and be the sort of thing that tips off Stalin, though whether that helps is questionable. Japan may also try to stick with the Dec 1941 timetable, but starting with FIC and the Philppines, with Malaya and the DEI as stage 2, trying to postpone war with Britain. All choices are bad, but waiting for that Two-Ocean Navy Act to be built is worse.