More banks are going to affordability rather than income multiples. If you can prove that you can afford to pay, they will often lend you the money. Other banks may lend up to 4-5 times.
You also have 'self-cert' where you declare your own income and the banks do not check - of course you may lie on your application form, but be aware that this is fraudulent.
With regard your deposit, it relly depends on the cost of the house you are looking at. If it is over 10% deposit, then lenders will be more willing to 'take a view', knowing that they have a good deposit.
It will also depend on your personal searches (ccjs, arrears etc) - if you have a poor history, then you will not be able to get such a high income multiple.
Hope this helps