A few things will make the answer clear.
A) HSBT took lottery money for masjid refurbishment BUT they took money also from the public telling them they have no funds. So the public gave money thinking HSBT have no money. So this was fraud. This is public knowledge for the locals who gave money that they claimed they have no funds.
The same was done with the money for the girls school, which they raised money from the public and when they were not given planning permission they sold the building and no one knows where the money has disppeared to.
Taking money from a harbi is legally permissible if he gives the money of his own free will, but lying to him is impermissible. It is clear for anyone who goes on to the lottery website that when HSBT applied for lottery funding they placed non existent classes and youth schemes in the application. If you go to the Trust you will find that none of these schemes exist!!
C) Even if one does take money from a harbi, it is impermissible to build masajid with that money. This is what the fatw books have pointed.
This is from my small knowledge of this issue, please feel free to correct me.