The 1972 Local Government Act did not anticipate pandemics or councils meeting online. One has to look at the wording of the statute and interpret it according to reasonable assumptions about what Parliament intended. What the statute actually says is that "if a member of a local authority fails throughout a period of six consecutive months from the date of his last attendance to attend any meeting of the authority, he shall ... cease to be a member of the authority".
Now, I would be very much inclined to argue that Parliament had in mind a situation where meetings were taking place, but the member in question was absent from them. I do not think Parliament envisaged a pandemic where meetings ceased. Bearing that in mind, I would read "fails ... to attend any meeting" as requiring that there was a meeting to attend during the period of absence. As there was no meeting at all in your situation, I would argue that the disqualification does not apply.
It seems to me the clerk is interpreting the statute in an inflexible way. If all, or almost all, councillors are disqualified, then the district council has to step in and appoint councillors. But in this case, the obvious course for the district council would be to simply reappoint the same councillors. So a lot of extra administrative effort would result in achieving no real purpose.
I would recommend pressing the clerk to look at the matter again, and seek to apply a constructive interpretation of the statute so that life can proceed in a practical way.