The rent-a-room scheme allows you to let part of your home and generate a tax-free income of up to £4,250 a year. This equates to a monthly rent of just over £350. Details here.
The government doesn't distinguish between homeowners and renters. As long as your landlord agrees, there's no reason why tenants shouldn't benefit by taking in a lodger too. Try MondaytoFriday for a room-share agency specializing in weekday lodging only.
This scheme also applies to being a host family for students. Check with your local boarding school, college, university or language school for overseas students requiring such a service. Often the students come from rich families paying to give their children the best education they can, so the 'quality' of lodger is high. Here are some options to consider:
Long term students, generally over 18 and from China, Hong Kong, Russia and elsewhere. They are usually very serious about their studies, don't need full time care during the day and after their evening meal typically go out to meet up with their friends.
Short term language students/exchange students, generally Europeans coming over to the UK to get a feel for our culture and do a short language course. They are usually quite young - under 14 is quite normal. The language schools usually place them in 2's but it depends on your space. Although they are under 18, they are out during the day at the language school so don't usually require full time care.
Mature students on short stays of anything up to 6 weeks. No long term hosting ties again, plus generally older students try and get to see other parts of the country at weekends, giving you more private time.
Your local professional football club. They often require host families for young footballers that they take on from other parts of the country or world and their rates are usually quite a bit higher than from colleges.
Potential annual earnings
£4250 tax-free