You can very much use a deed poll to change your name even if you are foreign - it's just a personal declaration or intent that you forward to different organisations. You can use general wording that's in the link provided by u/dontmindmyboobs

“I [old name] of [your address] have given up my name [old name] and have adopted for all purposes the name [new name].

Signed as a deed on [date] as [old name] and [new name] in the presence of [witness 1 name] of [witness 1 address], and [witness 2 name] of [witness 2 address].

[your new signature], [your old signature]

[witness 1 signature], [witness 2 signature]”

You can use a deed poll with your old passport or apply for a UK drivers license and use it as an ID. Highly unlikely you will get into any trouble for having a passport in a different name - you are not committing fraud or being dishonest. Good idea to also have a letter from a doctor about your gender reassignment.

The issues you might run into start if you want to go abroad - travelling with documents in different names outside of the the EU - BIG PROBLEM, inside the EU you are golden as long as you book stuff under your old name and keep your deed poll and doctor's letter with you.

However it's best to get the documentation sorted sooner than latter as you never know if some idiots in the UK win general election and pass laws on name changes or immigration that will complicate matters.

Also - if you decide to not use a deed poll you can change your title to mr on payslips / bank account as it has no legal standing in the UK.

I advise against statutory declaration as it has more serious legal implications than the deed poll - having said that - I think we shouldn't feel like criminals for being trans and using our proper names - its a shitty situation when you want to book a flight under a new name but you can't.