A mortgagee was still liable for payments, even for a damage or destroyed property, though building societies showed consideration for circumstances; there was a general payment moratorium for those in military service and in evacuated areas, and in cases where owners of damaged properties were unable to maintain full payments "... the building societies generally seek to obtain at least the interest due, but even this is not fully pressed." ("British Building Societies During the First Year of War", Federal Home Loan Bank Review, Vol. 7 No. 7 (April 1941))

This could be a particular issue as insurance did not cover bomb damage. Though Lloyd's had insured against Zeppelin (and other aircraft) attack during the First World War the increase in destructive potential of bombers between the wars led to fears of a "knock-out blow", a massive, devastating bombing attack using explosive, incendiary and poison gas bombs to cause such catastrophic damage as to render a country unable to fight. Such fears led to insurance companies excluding war damage from 1937; the government announced, prior to the declaration of hostilities, that it would pay compensation for buildings, furniture and clothing, but due to the pre-war estimates of catastrophic levels of damage and the more pressing requirement to prosecute the war the precise terms of compensation were left for post-war settlement.

The Blitz, though awful, proved to be less destructive than feared. With no obvious end to the war in sight and people in desperate need for assistance the chancellor first agreed to make advanced payments of compensation to families with an income of less than £400 per year, then introduced a War Damages Bill in 1940, a collective scheme of insurance in which all property owners paid a premium to cover compensation.

Around two thirds of people did not own their own homes, so property insurance was not an immediate concern for many rendered homeless, and outright destruction of houses was comparatively rare; in the first six weeks of attacks around 16,000 houses were destroyed, 60,000 seriously damaged but repairable, and 130,000 slightly damaged. Unexploded bombs also forced many houses to be evacuated, with over 3,000 UXBs by the end of November 1940 awaiting disposal. Repair of damaged houses was therefore a priority, with empty houses requisitioned for those who required rehoming.

There was compensation for possessions, but only "essentials" - furniture, clothing, tools that were vital for employment. Luxuries were not covered, though what constituted a luxury for one may have been essential to another - a music teacher's piano, for example - so judgements were made by the Assistance Board who administered compensation schemes. This could be an area of friction as the Board was established in 1934 as the Unemployment Assistance Board and its officers "had not been trained to develop skill in the treatment of applicants" with the shift to dealing with bombed-out civilians and "When they erred in the interpretation of instructions, they usually erred on the side of parsimony." (Problems of Social Policy, Richard M. Titmuss)

Inevitably not all claims were genuine; Joshua Levine's Secret History of the Blitz notes the case of Wallace Handy who, in 1940/41, made no less than 19 applications for the £500 lump sum awarded to those who had lost their homes. He was sentenced to three years imprisonment with hard labour, but many smaller scale claims doubtless were made - Levine also quotes Mary Brown who staffed an emergency assistance centre, where they had details of the exact location of bomb damage: "Somebody would say 'I was bombed out last night.'
I'd say, 'Where did you live, dear?'
She'd say wherever it was.
I'd say, 'Well, that was at least five streets away from where it happened, wasn't it?'
'Oh, well, I got me windows blown in!'
'That's not quite the same...'"

The War Damages Bill was passed in 1941 and ultimately some 4 million claims were made under the resulting Act, payments totalling more than £1,300 million and continuing into the 1960s, so the unfortunate mortgagee should have been able to get their home, or an equivalent, rebuilt, but it may have taken some time and bureaucratic wrangling to fully resolve.

Further reading:
Wartime: Britain 1939-1945, Juliet Gardiner
Britain's War: Into Battle, 1937-1941, Daniel Todman
The People's War: Britain, 1939-1945, Angus Calder
The Bombing War: Europe 1939-1945, Richard Overy