Most difficult this one. (BTW you gave the Non-Geo number !)   The registered address seems to be in London & they are called either or with the same lady doing the answerphone messages at both addresses.
BT, Yell and ThomWeb show nothing for the Skipton office, so although it's on the Google search results, it may have closed, but I doubt that BT & Yell are that quick !!

The Kensington website gives through the subsidiary TML Solutions.
Enquiries confirmed that the offices below deal with other agents, and not directly to the public.  

Kensington Mortgages	# Kensington Mortgage Co.  #	Kensington Mortgages
1 Providence Place	1, Derry St	1, Sheldon Square
Skipton	London. W8 5HY	London. W2 6PU
N.Yorks. BD23 2HL	Tel: 0207 3760110	Tel: 0207 2977600
Tel: (0870 5561040)	Fax: 0207 3962239
Fax: (0870 5561050)	# This Office is now closed  #

Any more that I find I'll add a note, so I hope what I've given you helps.

On the "Council of Mortgage Lenders" link, also shows the (London office)

0800 111020

# Note: this number is for use as the ~ not to talk to clients.

Then the last Google link that comes up is another for HOMELOAN Mgt. Ltd. giving the additional numbers:-
Tel:  01756 700127 (0870 6013200)
Fax: 01756 700258

# Confirmed HOMEPLAN Mgt. Ltd. administer , also that 01756 692000 and the numbers above are correct.