How do I get a copy of my full birth certificate in England?

Easily.  You apply for it online, send in the payment, and get the certificate.  I have done it not only for me, but, for my ancestors as well.

The GRO is the easiest and cheapest place and covered the whole of England/Wales, you can apply online, pay and it is sent in the post to you, https://www.gro.gov.uk/gro/content/certificates/Lo... or if you need it immediately, you write out an application form available from the local registrar, pay and collect it that day or within a couple of days, it is more expensive to do it that way and you have to know which registry office to apply to( if you get the wrong one and they can't find it, there is no charge)

Easy.. You need to request a copy of your FULL birth certificate from the Registrar of the city / county you were born in 

There is NO central database

Go to the local town hall where your birth was registered. - costs about £10

Order it from the register office in the district where you were born.  Local councils run register offices so google the council.

Otherwise, and this is likely to be cheaper, order online from the GRO.  https://www.gro.gov.uk/gro/content/certificates/lo...  Ideally you need the GRO index details but as you will know your own name and date of birth, they should be able to find the correct certificate from that.

https://www.gov.uk/order-copy-birth-death-marriage...