I disagree with earlier posters. You don't have to have a signed contract to form a contract.
If I say to you "I'll clean your windows for £20" and you say "OK" then if I go ahead and clean in the reasonable belief that you wanted me to then we have formed a contract and you must pay. It applies whether done verbally, in sign language, by jungle drums, written in blood or by email.
However, it doesn't sound like you have said "We'll do three cleans and on the basis that we will clean three times, we have priced at £90 per clean". Neither have you said "We'll clean your windows every four months for £90 per clean and you must give us eight month's notice if you wish to cancel". Nor have you said "We'll clean three times for £270". If you've said any of those, it's a different matter (but may not change your best course of action).
So, in the absence of those, you would have a great deal of trouble getting a court to agree that they were in breach of whatever contract you did form when you carried out the clean.
I'd suggest that you pick yourself up, dust yourself off and walk away a little wiser. It's not worth trying to enforce IMO, however correct or aggrieved you may feel. Spend the time you would have spent chasing this up in finding a better customer. And make sure you tell every windy in town who the management company are so there is a consequence for them; if they find it harder to recruit a cleaner they may think twice about shafting them.
Vin