We live in Britain, where there is a national lottery:
This is where many people, across the country buy lottery tickets throughout the week and at the end of the week a large cash prize is given to the person with the right ticket number.
25 percent of the profits made from the lottery have to go to 'good causes' this can go towards schools, building sports facilities or to community activities.
I am part of a Middle Eastern society that organizes activities (sports and social) for the local female Muslim community. We applied for a lottery grant and were given a substantial amount of money for these activities, however the council also gives grants but, much, much less than the lottery.
My question is: Is it Halal to take advantage of this money for the local Muslim community, bearing in mind that our children go to schools that may be partly funded by the lottery, and we may go to hospitals or sports facilities funded by lottery money. Also, we would not be able to run many courses or activities this year without this money.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. 
Is it Halal for Muslims to benefit from "lottery money" to support their Islamic activities?
In fact, "Lottery grant" offered to Muslims is Haram; its owner is not known and so it might be spent for good or bad goals. Yet in England, where Jews and Anglicans accept to allot "lottery grants" for building temples and churches, it is more proper such grants that be spent for what is good and on behalf of the public interests of Muslims. Furthermore, it is our duty to benefit from such grants for what is good if Jews and Christians will use them to fight Islam and make Muslims disbelieve in their religion.
Also, we should not say that we have to benefit only from Halal wealth and the lottery grant is not so. Know that the attribute of legality and illegality is related to one who earns the money, and not the money itself.
In Sahih al-Bukhari from Anas that the Prophet (Sallallahu Alaihi wa Sallam) when he was given meat that which was already given to Barira as Sadaqa, he said: "It is a Sadaqa to Barira and a gift to us" . This indicates that illegality is not proved by the money itself.
Another evidence is that the narration of Ahmad concerning the roasted sheep that was offered to Allah's Messenger (Sallallahu Alaihi wa Sallam). When it told to the Prophet (Sallallahu Alaihi wa Sallam) that it was Haram, he said: "Give it to the captives as food" . al-Iraqi said: 'This Hadith has a good chain of narrators' .
A third evidence is Abu Bakr 's bet with non-Muslims of Quraish, with a previous permission of Allah's Messenger (Sallallahu Alaihi wa Sallam) concerning the coming victory of Romans over Persians, and when - by Allah's Favor - the Romans defeated the Persians and Abu Bakr received an amount of money because of the bet the Prophet (Sallallahu Alaihi wa Sallam) said: "This money is Haram, give it as a charity" . al-Tirmizi who said, 'it is good' .
Thus, according to the above-stated sound evidence, we say that we can get rid of Haram money in spending it in the public good interests.From a rational point of view, we state that such Haram wealth might be spent (1) in bad interests, (2) good interests, or (3) we spoil it. Since we believe that the first and third choices are Haram, so we have no recourse but the second choice, i.e. to spend it in the public good interests. 

Sheikh al-Islam Ibn Taymiyah while commenting on money whose ownership is not known, such money should be spent on behalf of the commons, because people may get money that they know is illegal due to its being taken unjustly, or through theft, or treachery, or usury, or gambling, and its specific owner is not known exactly.And according to Ahmad, Abu Hanifa, Malik and the predecessors in general, such money should be given to people who are most eligible for it.

But al-Shafi'e believes such money should be kept, not spent at all.However, a situation concerning "lottery grants or money", we have two choices, either: (1) Muslim take that money or (2) Jews and Hindu take it. Thus, we believe it is better for Muslims to receive such money and spend it on behalf of the most deserving of people and the public interests and in good activities, and this is the opinion of al-Salaf (predecessors) in general.

Imam al-Nawawi while commenting on dealing with Haram money received from a ruler, in his book al-Majmu' recorded the following from al-Gazzali : 'Some scholars believe that such money should be returned to the ruler since he knows its proprietor, and not be given as Sadaqa. Other scholars say it is better to give such money as a Sadaqa if one knows that the ruler will not return the money to its owner, but this will increase the ruler's injustice' .
Here, we state that returning "lottery grants" to the British government will support disbelief. 
al-Nawawi added: 'If one thinks than the ruler will spend such money on wrong actions or if he believs that strongly he has to spend it himself on the commons, i.e. public interests of Muslims, such as in building, archways and so on, otherwise, he can spend it little by little according to those who are in need' .
As a result, we state that Muslims in England have to take such grants, and to spend them on behalf of the public interests of Muslims. Such a position is required by Sharia evidence, rational deduction and making a balance between "Interests and causes of corruption".

Allah knows best.