I have registered a trademark before and it is not that straightforward. You have to advertise it first and go through quite a strict process.
I think there is also a period where there can be an appeal. I'm not 100% on this, but I seem to recall it is quite a process. I think if there are any old trademakrs that predate it, they will be valid so it would be worth checking club archives.
Also, I thought a trademark was a logo, not a piece of text. Have they trademarked the badge? They can't trademark a word in the english language as far as I know.
Would it be worth trying to raise some money from the fans (maybe a new specific pot) to pay a trademark specialist to advise us? Maybe there is someone amongst the fans that can access some trademark advice cheaply? I imagine we would need a few hundred quid for some preliminary advice and that may be enough.
In terms of breaching a trademark, I am not sure what the penalty is. I think it may be just loss of income and I imagine that if we as a club ignore the trademark ruling, they can only come at us for loss of income which they would need to prove. I'm not sure we would lose them any income, so they probably couldn't claim any losses.
If they went for an injunction to stop us using it, then maybe we could play as Streatham Rovers for a few games whilst it is sorted out.
I could be (probably am) wrong on some of this, but it may be worth looking into.