Is there a free reverse lookup web site for UK telephones?
How about any of these ?
Nope. Sorry, didn’t help. 
Anyway, a friend of mine was called by a number starting with 015547xxxxx. Is this a mobile phone?
Nope, not a mobile phone - definitely a land line. Try BT’s website - www.bt.com
Thanks! It says that area code 01554 is from Llanelli. Where the heck is that? 
Wales.
Probably a call-centre, it’s the only employment in south Wales these days
D&R
Anyway, the problem you were having is because reverse directories are only run on an opt-in basis in the UK.
Otherwise they’d be the burgular/stalker’s best resource.
I’m always getting wrong numbers on my mobile and home phone. Today I got one from Eurocars. I was surprisingly ready considering the time of the morning.
“Good morning, Eurocars”
“Er, I think you have the wrong number”
“Is this [number]?”
"Yes, But I wouldn’t have a reason to be called by ‘eurocars’ "
“There is an order for a 106”
“Not by me”
“Ok, sorry about that”
P.S. All UK mobile numbers start with 07.