the solicitor is the executor. Is that common?
Widespread. But let's not go off topic.
Respectfully Brendan, I don't believe it is at all widespread.
However, we don't need to prefer my opinion over yours, because this is a factual matter and the public data can be accessed by anybody on the courts website.
It is easy to get a list of all grants of probate or administration issued in the past year (or any year). This includes the name of the deceased, date of death and the person who obtained the grant (i.e. who is the acting executor or administrator). That information is available at no cost on the courts website.
It is equally easy to take such a list and google the names of each person who obtained a grant to see (with reasonable accuracy) how many of them are, or are likely to be, solicitors.
Within that small subset of names who might be solicitors (and in my opinion it will be a small subset) some of them will indeed be solicitors who were named as executors in a will. However, many of them will be solicitors who were not named in a will but who are acting under a power of attorney for a non-resident executor (the grant of probate in such circumstances will issue to the solicitor).
I would be astonished if the 'possible' matches came back at any more than 1 in 20 (and the actual matches would obviously be a subset of this).
EDIT: this exercise would not harvest data for solicitors who had been named as executors in wills, but who had renounced their executorship.