I've always used Thomas Exchange, in the arcade opposite MacDonalds in Liverpool Street.
I went to Portugal in June and got 1.17, but today their rate is almost identical to Ace FX, so I'd go for whichever is closer, or easiest to get to.
I'd try never to use the places at airports, always a bad rate, but it's your call.
The very best exchange rate is from a bureau de change called Best Foreign Exchange www.bestforeignexchange.co.uk. You have to order it online, but can collect it seconds later from one of their branches. Their rate is head and shoulders above the rest. By way of example, the highest alternative on the day I bought my euros was paying €1.12 for each pound, whereas BFE was paying €1.16. It adds up.
However, as bmovie says, the Travelex desk in Tesco Surrey Quays will match their rate - which I have done in the past - but it is a bit of a kerfuffle as the staff have to call their head office to get authorisation to match it. Worth doing though if you can't get over to one of BFE's branches.
No affiliation with Best Foreign Exchange. I found them on MoneySavingExpert about four years ago and have used them since.