It would depend how quickly the invasion was defeated... If I was in charge of the British army, I wouldn't push them into the drink right away, I'd let them pour more men in so I could capture more after the RN cuts their supply lines.
Best case for the Germans (whilst still being defeated) the first wave (maybe abour 3-4 regiments) is utterly destroyed along with their "assault" shipping and they cancel the whole enterprise
Worst case, they land 8-10 divisions, suffer heavy casualties en route, AND have those that land run out of food fuel and ammo and be compelled to surrender
All in all it would mean nothing. 8 divisions is a flea bite on the German army... it might actually make things worse for the British in the long run; Hitler could get some serious revenge desires going which could include but not be limited to closing Gibraltar (without Spain's approval) or committing serious resources to the med to capture egypt)... or he might suck it up and move on as otl...Barbarossa wouldn't have to be delayed in any serious way since Garrison divisions in Norway, France and the Low countries could be combed out (as was done later) to fill in any necessary manpower vaccumes
The British may or may not be inclined to send more troops to the med... it depends on if there is a fear of renewed invasion keeping aircraft, troops and ships in place