You can start searching Youth Hostel information at:

http://www.iyhf.org/iyhf/ehome.html

The only hostels I have stayed at in the UK have had some different rules than those in which I stayed on the continent. In some of the UK hostels there were all day lock outs. This can be a real pain if the weather is bad. Also you will likely be required to pitch in with cooking or cleaning.

I would also recommend that you book ahead if you are going during the summer months.

I have never stayed in London hostels so maybe someone else could comment on safety and cleanliness here.

Jude