A Tory official in Ealing Central and Acton, another Remain-backing London constituency that is second on the hit list, wants a “Tory with a heart”.
The tight timetable should help Mrs May to choose sympathetic candidates.
Normally, local Conservative associations spend months carefully choosing their parliamentary candidate.
Activists tend to be to the right of the parliamentary party, and most would dearly love to choose hard-Brexit candidates.
Garry Heath, a member of the Wycombe Conservative Association, wrote on the ConservativeHome blog that the Tories should “purge our party and deselect the Remainers”.
Yet with the election only seven weeks away, there is little time for local parties to scour the land for suitable hardliners.
Conservative Central Office is expected to step in and present local associations with a shortlist of candidates.
These lists will reflect Mrs May's politics; in turn, the candidates will be loyal to her if elected.
The easiest option in many cases will be simply to reselect the candidate who stood in the 2015 election.
Back then, most of the party's leadership was in favour of Remaining, albeit reluctantly.
Whatever happens, it looks as if Mrs May's prospective new MPs are unlikely to give her too much trouble.