First up, stick to something under 250 grams flying weight. No licence or other interference needed. There are models from a website, FliteTest. They do plans, the models are mostly foam sheet construction. There is a good forum attached. Have a read
Another possibility is the RCM@ E forum. They have a long-standing thread on converting the Lidl foam chuck gliders into radio controlled slope soared, powered gliders, to things that look like a Warthog. The basic airframe is about £8. You can, buying a second hand transmitter, micro receivers, micro servos, LiPo battery charger from the the Far East, you might achieve the £50 barrier. But it’s a steep learning curve, and on a tight budget, a potential minefield for fakes.
I do radio control, but my stuff is bigger, and I’m not an expert at that end of the game.
Just one word of caution. Building a radio controlled plane from scratch, sorting out the radio, and the trimming of the airframe, and snagging to get success is not an idle wish.