Usually the brackets, of mortgage payment rates, change on 5, 15 and 25%.
So if you pay 5% deposit they won't offer you a better rate APR unless you can pay 15% up front.
It's the main reason you'll see most people trying to pay a 25% deposit to get the best rates.
Not directly what you asked but if you're thinking of buying a place here's what I did to find out what I could afford.
Think not so much about how much money you have now, but think how much you can afford to pay back.
So say you can comfortably afford to pay back ~£550 a month.
Put some numbers into here (
http://www.moneysavingexpert.com/mortgages/mortgage-rate-calculator) with a standard APR of say 4% (worse case scenario) and keep changing them until you are paying back what you can afford each month.
You should end up with something in the region of being able to borrow ~£105000.
Add £105000 to whatever deposit you have (£60000) and you have £165000.
Now what I did was take off about £4 to cover my legal fees as well as moving and furnishing costs. So to be on the safe side I'd say take of £5K to cover all your costs.
So if you were willing to pay ~£550 (actually £554) a month then with £60K deposit you can afford to be looking at houses in the region of £160,000.
Hope that helps!
Roy
EDIT:: Worth pointing out that rates from lenders change on a daily basis and looking at something now it's likely it won't exist in 2 weeks time. There's also talk of the banks getting rid of fixed rate mortgages at the moment due to the predicted bank of England increases.