As you are unemployed now and i assume will be making a claim for benefits in the interim, ask the benefits advisor for information on starting up your own business.
While you would not qualify for it yet I spoke to my benefits advisor about starting up happy House Cats and she got me on a business development course run by business gateway, that was a 6 months course where I got jobseekers + a tenner a week and had to attend the business gateway every week instead of signing on at the jobcentre.
The course included a selection of useful seminars and one or two day courses in accounting, advertising, e-commerce, taxation, creating a business plan etc etc etc. It helped an awful lot for me, some things more so than others, but the end result is a year later I am managing to make a living from the venture and the reason I am here on this forum is I am now expanding from cat toys (which I now have a european wholesale distributor for and am paying others to make for me) and jackets into cat wheels, wooden beds and cat furniture.
While you will unlikely be eligible for the course proper (get benefits + tenner) it may well be that as an unemployed person you can get onto the the course or at least get some free assistance from Business Gateway or your local equivalent.
When I started the course last June I had been unemployed and trying to find work as a spark for near on 3 years, I was down to my last £200, I started happy house cats with that, well half of that really, but I put 70 or 80 hours a week into it.
If you have the determination you can make it, find a niche and provide a quality service - that includes turning up on time, answering calls and questions, treating people with respect and you will find word of mouth will quickly bring you enough work. Turn up late, don't answer the phone, do a less than perfect job and word of mouth will very quickly ensure you get no work. To be honest from my experience of tradesmen and stories I have been told by customers it is not really too difficult to shine brighter than most if you put in a bit of effort
By the way, I think you will find leaflet drops the least effective means of advertising, 99.5% of leaflets dropped through doors will go directly into the bin without even being read, I know of two people who did leaflet drops of 5,000 leaflets and one got 5 jobs from it the other got 3.
Although elderly neighbourhoods is a good place to find handyman/ tradesman work, and you will find if you get one or two jobs in such areas you will very likely get called upon by others in the area - I do quite a few odd jobs and bits and peices for elderly people who live near my workshop, mostly I only ask them for a token amount as they are really more neighbours and friends but they always offer what would be a very reasonable wage if I took it - Another bonus being bacon rolls, meals, cakes, cups of tea and coffee, bless em
Good luck