To canoe on the River Medway between Tonbridge and Allington you need either a River Medway Licence issued by the Environment Agency - cost £23.76 per annum (2010 rate), or just £4.87 for a one week licence (minimum available).
 
Alternatively you could buy a BCU licence for around £32.75 per annum (2010 rate) which means you can canoe on all waterways run by the Environment Agency or British Waterways, plus you receive 10 canoe magazines per year, discounts at certain stores and third party insurance.