I don't think there is any collusion between US and British embassy to share the out of status information however, they may have made provisions for this after the 911 attack. You do, however, need to answer whether you have overstayed in other countries while filling out the visa form for UK where you definitely will have to lie and also you will have to lie about not going to USA as they will definitely check that information with American authorities to verify that you have not committed any crime. Otherwise there is no way you are going to get the visa. My mate from Hungary did the same more than ten years back and came here but I don't know how things are these days because of the advance in IT. Also, your pp will have landing information on it when going back to Nepal  and you will have to sort that out too. Its difficult but not impossible if you have no bad intentions.