We are UK citizens in USA since 29 January travelling on a recently acquired ESTA and 3 month waiver programme on a compassionate visit overseeing the care of my wife's sister who is back home recovering from treatment for incurable cancer. We know we have to leave USA end 29 April . We have British passports . We intend to travel to Mexico for 48 hours. Will we need visas for this in order to be allowed re entry to USA?
If you are trying to extend your time in the US by traveling to Mexico, that is unlikely to work unless you apply for a B-2 visa while you are in Mexico.
If you want to go to Mexico for 48 hours while still intending to leave the US before your I-94 expires on 29 April, there should be no problem.
You should probably check your I-94 to be certain of your departure date. April 29th will be your 91st day of presence in the US after arriving on January 29th, and the US appears to be counting the 90-day period inclusively in recent years. It's possible that they've been applying that policy inconsistently, however.