To ride a 125cc motorcycle or scooter in the UK you must be at least 17 years of age to ride on L-Plates, a provisional licence and a current valid CBT certificate are required first. There are unfortunately no "grandfather" rights meaning everyone over the age of 17 must complete a
CBT course. A better long term option is to take and pass the full A1 test, then you never have to take a CBT again. All A1 category motorcycle are limited to a maximum power of 11 kW (14.6 Bhp). When you are first starting out, then a good secondhand Japanese bike can currently be bought for around £1000 - £1400. These will hold their value for a long time as long as it is looked after, regularly serviced and cleaned! If it is in good condition and has been looked after, it will provide you with cheap reliable transport for years to come.
Some good examples to look for are, Honda CG 125 (2001-07) KTM Duke (2011-15) Yamaha YBR 125 (2005-12) Honda Varadero XL125V (2001-09)