London flat

It seem that in order to have a place to reside in London when at the court (but also to probably ensure housekeeping) Elizabeth lended Sommersett House (look at it the current building is quite beautful, though I couldn't manage to find what it look like in 1574 at best here 17th century) technically the place was still royal property (unlike Hundson house who was all Henry) . The estate was kept in the care of his family even after his death as his wife was made keeper shortly after.