The above is a popular argument, repeated for example by John Redwood (who is right more often than he is wrong).
If private sector debts are expanding much faster than GDP, that expansion will contribute a significant amount to aggregate demand. And that rate of debt expansion cannot go on for ever.
However, as long as that level of demand expansion does not cause excess inflation (which it didn’t prior to the crunch), there is no obvious reason to think the rate of demand expansion and ECONOMIC GROWTH (as distinct from the rate of debt expansion) cannot continue.
So the explanation for poor UK economic growth since the crunch has to be more subtle than “debt expansion is no longer contributing to demand”.
A possibility is that much of the debt fuelled construction which is a relatively low skill activity. Put another way, if economic growth is to continue at the pre-crunch rate, the growth must come from more skilled forms of economic activity, and the relevant skills just aren’t there.
But even the latter idea is doubtful in that there is evidence from the US that construction workers have found no more difficulty finding alternative employment than workers losing jobs in other sectors of the economy.
Another possibility is that the large majority of inflation is cost push: i.e. government could perfectly will give the economy a decent monetary plus fiscal boost, and the effect would be to boost growth rather than inflation.