NWIFlyer

We really need to know the likely size and weight of your carry on bags.

BA - out of LHR and LCY - will have the most generous allowance. If you can lift it into the overhead, you'll be able to take it onboard (or, worst case, get it checked for free if the overheads are full). Forced checking is far more likely at LCY where BA operates Embraer E170/E190s and therefore overhead space is at a premium. BA offers both Business Class and Economy (but be aware there is no lounge at LCY and no blocked middle seat because of the 2-2 seating). In J you'll get a 3-course cooked meal, in Y a small snack (which could be a packet of nuts, crisps or biscuits, or a breakfast roll early in the day) and drink (which can include alcohol).

EI, out of LGW and LHR, is Economy only. Carry-on baggage is limited to 10kg, and EI have been known to weigh it - and they may well charge you if it's over, although I have no direct experience. If you eat or drink anything on board, you'll be charged for it - EI is to all intents and purposes a low-cost airline now, essentially no different to Ryanair.

Cityjet (WX) has a 12kg limit, and flies Avro RJ-85s - so there's less pressure on overhead space with the bigger bins. They also offer a free checked bag if you're over the weight limit. Again, free food and drink.

You can also use Ryanair (FR) from Stansted and Luton, but it sounds like that doesn't really fit your location as well.

So far as delays are concerned, both LCY and LHR are susceptible - due to capacity at LHR and weather at LCY. If that is an overriding factor, you need to be on FR ... but there are other downsides which might well overrule that!

I also notice you're a UA Gold. If you have a lounge pass as well, you might be influenced by the fact that EI flies from T2 at LHR, and there's a simply superb (yes, really ...) UA lounge in T2B. You can't use it by dint of flying EI given they're not a Star airline, but presumably you could on the basis of a United Club membership.