I used to work for UK Border Control but retired some years ago so what I say may not now be the up to date position.
That said, having more than 1 passport is very common and it is entirely up to you which one to use. You are not obliged to renew the British one if you don’t want to. However what matters is what you intend to do in the UK. With the exception of Irish passports which allow a general right to reside in the UK, all other EU citizens are now subject to conventional immigration control. So if returning to the UK to resume residence, you would need to demonstrate you had that right. Otherwise you might be subject to a time restriction and a prohibition on employment or even refused entry.
You haven’t said where you were born but assuming it was in the UK, birth in the UK in itself does not confer British nationality or even a right of residence, so having a UK birthplace in an EU document is not sufficient proof of the right to live in the UK. Additional documentation is required.
There used to be a document called a “Certificate to the right of abode” (issued by the Home Office) that you could get endorsed in a non British document, to show you had that right. That would enable you to pass through the UK controls without difficulty. However it costs more than renewing your British passport so you may not feel it worthwhile. You could also show the Immigration Officer your expired British passport as proof, but as has been said, that’s going to be a slower process. You also need to be aware that if you show an expired passport at check-in the airline may not carry you. So you would need to carry both documents.