I have recently moved from India to the UK and carried a Philips air fryer with me. The plug on this appliance is marked 16A 250V. Wattage is 1425.
The marking on the plug is the current rating for the plug, not the current the appliance will draw. 1425W is just under 6A so it should be fine to use the appliance on a 13A UK socket.
Sometimes you do find appliances (especially ovens) that draw a bit more than 13A and can therefore be a PITA to connect safely in the UK but it doesn't seem your case is one of them.
I'm not too comfortable cutting into the power cord and replacing the fused plug.
My advice would be to change the plug, it's really not difficult and more plugs and sockets in the chain mean more things to go wrong.
Do you think this product will work? http://www.cableuniverse.co.uk/13a-16a-fly-lead-converter-13a-plug-to-16a-socket.html it says it's used for hooking up caravans to household mains but it seems the end purpose is the same i.e. plugging 16A into a 13A source?
The link is broken but a cable sold as an adpaptor for caravans is almost certainly NOT the correct adaptor for your needs.
There are many different types of plug in the world. Just because two plugs have the same current rating as each other does not mean they are compatible with each other.
The indian and south african 16A plugs are equivilent to the 15A BS546 plug1. In this UK this plug is mostly used for stage lighting. Stage lighting suppliers will be able to aupply an adaptor cable ( http://shopwl.com/13a-to-15a-adapter/ ) but they don't seem very cheap (I did spot a used one on ebay for £5 but I won't bother linking it because ebay links go stale really quickly).
Caravans use a totally different type of plug, the 16A blue IP44 single phase IEC60309 connector (often reffered to be UK electricans as a "CEEFORM").
For the beneit of other people reading this question note that the 16A "SCHUKO" plugs used in mainland Europe are different from both of the above types.
1 Similarly the indian and south african 6A plugs are equivilent to the 5A BS546 plug.