I think the the schools and LA are probably obliged to test these late applicants as per the School Admission Code. The School Admissions Code states
https://assets.publishing.service.gov.u ... 19_Dec.pdfQuote:
2.9 Admission authorities must not refuse to admit a child solely because :
a) they have applied later than other applicants;
b) they are not of the faith of the school in the ca se of a school designated with a religious character;
c) they followed a different curriculum at their previous school;
d) information has not been received from their previous school; or
e) they have missed entrance tests for selective places.
They are facing a disadvantage as the places are already full but it could impact the waiting lists.