I could have to move down South (just outside North London) from Yorkshire for a possible new job.

Does anyone have an idea how much I should be asking for to relocate?

Move down to the South? If it was me, it would be more than they could possibly afford..

Same applies the reverse way druidh – great to see the divide is still so strong.
Teapot £5k – £10k for relocation costs depending on your personal circumstances family etc

All moving costs plus rent paid for until you find a place, petrol and time of work to view property, it will cost them a pretty penny, IIRC mine was about £15K 5 years ago

One of my friends has just relocated albeit for a internal move within the company – so things may be a little different. As far as I can recall it was less about a single figure but more about what items the company would cover – e.g. stamp duty, legal fees, moving expenses etc. but overall I believe it was close to £25k.