The 13 A on a UK plug means that the plug is rated to carry a max of 13 amps. The largest fuse which can be used in this type of plug is 13 amp. A 13 amp fuse doesn't blow at 13 amp. This is the current it will carry without blowing. Once the current exceeds 13 amp, the fuse will eventually blow. The greater the current exceeds 13 amp, the quicker it will blow.
Lower powered appliances use lighter gauge flexes and the appliance itself may incorporate thinner wire. For this reason a lower rating fuse is used in the plug even though the plug has a 13a rating.
It is always dangerous to replace a fuse with a type which has a higher rating. The fuse is there to protect cable and appliance in the event of a fault and is the "weak link" in the chain, preventing a potential fire.
If a fuse keeps blowing, there is likely to be a fault in the mower. Possibly something is producing excess friction in the motor and this is causing a surge on startup which blows the fuse.
Euge
January 2013