Well, that depends on how many Anglo-Saxons still arrive; if they come in numbers anything like OTL, they'll simply displace the British Romance language entirely with an Old English analogue. If they don't arrive in strong enough numbers to displace it, they likely won't influence the language any more than contribute some vocabulary that didn't exist previously in Brit. Romance (for example, my amateurish attempt to Latinize the O.E. word Weregild might be something like Gueryilde), and continue using their language separately.
Incidentally, here's the Our-Father of that language I listed before that's a sorta-mix between French and a Brythonic language;
a Phazeoir Nusteor que bias 'n y ceues;
foreth noef il tew nom;
gouenyes il tew camouil;
foreth fès la teva gouoluntáts en lâ derra cuomo 'ny ceues;
danos-el osdia le nusteor panèn cuotidièn;
dimeti y nusteor dheuz cuomo dimitemus ai nusteor dheutoeres;
et ne nus attrayer rhen al tentación, mays eliveránus des val.
Padraic.