BA: The children are adult passengers. No UM issues at all.
AA. The younger child must travel as a UM unless accompanied by someone 16+. The older one may travel as a UM if you wish.

I would strongly urge you to book nonstop flights. This is especially true during the pandemic when cancellations & schedule changes are frequent and may create awkward logistics issues. Thus, LHR-BOS.

Whether to fly AA for its UM service is a matter for you to consider in light of the childrens' maturity. There is nothing complex about this journey and BOS is an easy arrival point. Presumably an adult will pick them up at BOS.

It should go without saying that you should not book anything not full refundable until and unless the US changes its current exclusion rules for the UK. Those may well not come until the fall or later and will likely also require full (2 doses for 2-dose vaccines) vaccination.. But, as it stands, if they are admissible to the US, have their required negative Covid-19 test result in hand and can answer simple questions if asked, there is little that UM service will provide older teens. CBP is careful about human trafficking concerns and thus, it is a good idea for whoever is meeting the children and for you to both be available on mobile at the time when the children are processing at CBP in BOS. If there are any questions, best to deal with them on the spot.