If it's after the Fall of France, the UK gets a significant air combat bonus (via "Their Finest Hour" decision) for the next 6 months or so. You really don't want to engage UK fighters during that time period, if you can avoid it. Before that, Germany typically has a technological advantage over France and Poland due to its high starting tech levels and sufficient Leadership to maintain that lead, but NOT over the UK, so you're taking on an adversary with an equal starting situation and the Leadership to keep its research current or even slightly ahead of time. Anything you do that's less than "optimal" will leave you at a disadvantage against them. Then they get the TFH bonus on top of that.
As pointed out in the previous post, stacking penalties are a very important but poorly explained phenomenon (each plane gives a 10% penalty to ALL planes in the combat, except for some missions where you only suffer 10% for each ADDITIONAL plane), so you really don't want more than 4-5 planes per combat under most situations. Three planes gives the highest offensive firepower (4 for some specific missions, and some naval missions only incur a 5% penalty per plane, making 6-7 the optimal number), but a 4th or 5th plane can sometimes help split up incoming fire enough to make it viable through sheer survivability, even though it does less damage to the opponent. That's assuming that your airfield can repair that many planes at a time (1 per airfield level). Note that it's possible to amass a huge number of aircraft and gain a higher total damage figure, because stacking penalties are capped at 90% and 30+ planes will provide SLIGHTLY more firepower than 3 in spite of the massive penalty. I'd much rather engage the enemy in 10 different locations with 3 planes each, rather than tie up 30+ planes for one attack.
The other point to consider is doctrines. If your fighter doctrines aren't up to date, you've got less Organization, which means your planes run out of ORG first, and start taking additional Strength damage (which requires time and IC-days to repair). During an air combat, pause the game, click the combat progress bar below one of your units, and check the relative ORG values of your planes versus the UK's. Check the modifiers for each unit. You should be able to see where and why the combats aren't going well.
The Intercept mission provides a small but significant bonus to air combat, so using Intercept instead of Air Superiority is more effective, and also allows the planes to repair overnight if there are no enemy planes in the area. Air Superiority doesn't always allow "down time", so your planes frequently skip a repair cycle.
Note too that the Defensiveness and Toughness values for aircraft are all but irrelevant during air combat, due to a mistake in transferring values from HOI2 to HOI3 (the later game used percentages, the earlier used decimal fractions), so instead of giving a 5% increase per tech level, you only get a 0.05% gain, which is pointless. Game balance was set using those wrong values, so fixing the mistake would involve a complete rebalance of air combat as well. The mistake was fixed for land combat values in one of the early patches, and combat balance was readjusted for it, but air combat was never corrected, much to everyone's dismay.