I’ve found bank statements and utility bills with the name I’ve applied for my passport in ,and in my married name ,
I’ve been using my name this way for 20 years ,so I didn’t expect a problem,hopefully this will be enough
Otherwise I will do a deed of name change.
OP, in everyday life you can use any name you like, provided it isn't with intent to commit fraud, but that won't be your legal name.
You must have opened your bank account/s when checks were less stringent, as today you would need to provide official ID bearing your legal name.
Your legal name is the one on your birth certificate, unless officially changed.
There's a useful rundown on the Net Lawman site, which seems reliable ww.netlawman.co.uk/ia/changing-name-passport
It says "If you apply for your first passport under the name by which you are known (and want on your passport), but that name is different to the one on your birth certificate, you should complete a deed of change of name as evidence of your name."
So as this is your first passport, you will need to complete a deed of change of name.
And I second the advice by a PP on checking the validity of your marriage certificate.