It’s easy if not quick – we used an agency who give you official looking documents, but really they’re snake oil, you just start using the name and it’s legit – the documents do make it easier though with some people.
It’s worth noting that all places will accept it – my Son for example has my surname now, on all his school books and on the register he has our name – but on thier official records he’s still got his mothers maiden name. His next passport will have our name, his driving licence will too – but it’s likely his NI card will have his old name, as will any records held with NHS. It can all be changed but it’s a PITA.
As for OP, if you had your name changed, does your Birth Certificate reflex your original name? You may not have to go through so many hoops.