Tonker - this is purely my understanding, based on my experience with HMRC and my Accountants over nearly 40 years as a UK expat with mortgages (now history, thank heavens!).
Most importantly, you need to seek Professional advice before making any decisions - expat tax is a minefield.
Here's my take on your question though. I don't believe the simple fact that you have a mortgage with a UK bank or Building Society on a UK property would affect your Resident/Non Resident status with HMRC. (It could potentially affect your status as Domilciled/Non Domiciled, but that is a much more complex issue). However, if your wife/kids continued to occupy the property in UK, and/or the property continued to be available for your occupation on visits to the UK (even a single room) then your tax status and liability could be affected. Secondly, if you rented out the property once you'd moved overseas, and kept the mortgage, as a landlord, you would not get tax relief for the mortgage interest which you pay - that was removed last year. I'm open to correction on any of the last paragraph - if anyone has any more definitive information, I'd be interested to hear it.
Finally - go to the HMRC website (hmrc.gov.uk), and look at the documents referring to "Residence/Non-Residence", and anything relating to the "Statutory Residence Tests". More effective than OM-A for those nights when you need to sleep before a flight, but very informative if you persevere! But as I said - get Professional advice!
Good luck,
7B