I am married and have two daughters but I have not registered as a married person in the UK yet as they still think that my wife is a single mother and she lives alone and they help her paying the rent of the house where we live, and the reason is that if I tell them about our marriage they will stop paying rent for the property we live in as it is so expensive and we can't afford it.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If your marriage with this woman was completed fulfilling all the compulsory condition of an Islamicly valid marriage, the most important of them being the presence of the guardian of the woman and the witnesses, then she is your wife. Registering the marriage in a court is not compulsory for its validity.

If the grant is given on the condition of not being married then you are not allowed to benefit from that grant. A Muslim has to fulfill the conditions of contracts he/she commit to. Allaah Says (which means):  {And fulfill [every] commitment. Indeed, the commitment is ever [that about which one will be] questioned.}[Quran 17:34]

High cost of rent or the authorities being non-Muslims are not Islamic excuses to receive such grant without fulfilling the condition of being entitled to it. Know that whoever fears Allaah, He will relieve him from every grief and facilitate his matters. Allaah Says (which means): {…That is instructed to whoever should believe in Allaah and the Last Day. And whoever fears Allaah—He will make for him a way out. And will provide for him from where he does not expect…}[Quran 65:2-3].

We draw your attention to an important matter, that hiding your marriage may result in the loss of some rights, or you may become entangled in problems, or it could give a poor impression of Islam if the government discovers the reality of your case.

Allaah Knows best.