I have just applied for a loan and they have asked for me to send £50 admin fee in order to complete my application! Is this a scam?

Might be.

Where is the loan through? How did you hear about this? What info have you given them?

What are the terms of the loan? More info helpful.

Normally fees would merely be deducted from the loan proceeds.

I do hope this is not an internet thing

RUN, don't walk.
This isn't a classic scam, but a seriously unhanded tactic.
They advise that they can get you a loan at rate X but need an admin fee.

You send the info back and find that you are refused for loan at X and all they can offer is rate Y (10% higher) or none at all.

You should never have to pay to setup a loan.