You haven't said whether your bitcoins are in your bitstamp account (risky over the long term!) or at an address in your own personal wallet, so I shall assume the latter.
When you log in to your bitstamp account, you should be able to find
a "deposit" page with instructions for various ways of depositing
into your bitstamp account. On of those ways will be “bitcoin” —
the “bitcoin deposit” page will tell you what bitcoin address you
need to send your bitcoins to in order for them to be credited to
your bitstamp account (they give you the address as a string of text
and as a QR code).
Having found out your bitstamp deposit address, you then go to
your own wallet (you haven't said exactly which wallet you're using,
but I mean the thing that you're calling your “blockchain wallet”).
You instruct your wallet to send your bitcoins to your bitstamp
Some time later, your bitcoins will be credited to your bitstamp
account (could take a few hours for them to show up). Keep an eye on
the BTC balance of your bitstamp account.
Once your bitcoins have appeared at bitstamp, you can sell them for
Euros or US Dollars. Bitstamp don't support GBP. I tentatively
suggest you sell for Euros because a SEPA transfer into a British
bank account is usually cheaper than a USD wire transfer (but check
what fees/exchange rate your bank charges!). You can either use
a market trade to sell them at the going rate, or use a limit
trade to offer them for sale at a price that you hope someone will
be willing to pay.
Having sold your bitcoins (on bitstamp) for Euros (or perhaps US $), you then have
to go to bitstamp's "withdrawal" page and tell bitstamp where to
send your money (i.e. the details of your GBP bank account).
Obviously, you need to follow bitstamp's SEPA instructions if you
sold for Euros, or their USD wire instructions if you sold for USD.
If your bitcoins have been sitting in your bitstamp account all along, then you can omits steps (1) to (3) above — your should be able to figure out from your bitstamp balance if this is the case.
EDIT: If you bought your bitcoin before the hard fork, don't forget that you should now also own a BCH (especially if you kept your bitcoin in your own wallet),