1 The Queen does not have to pay tax, therefore she cannot avoid or evade something she doesn't have to pay.
2 HMRC stands for Her Majesty's Revenue and Customs, any tax paid by the Queen (voluntarily) is her paying herself.
3 HMRC have outsourced their property to Mapeley (DYOR)
4 Oh, and this....
Labour rent their London headquarters from a tax exempt property unit trust fund based offshore in Jersey: https://t.co/DWZ3FiHi0Z— Alex Wickham (@WikiGuido) November 6, 2017