First welcome to the forum.
Next £50 for the antenna is plenty. However you will need decent coax especially if the run to the antenna is say 5 meters or more. And you will need a method of mounting the antenna, so a bracket & mounting pole too.
Coax is around £1.50 to £2 plus per meter. And you will need a connector each end of the coax. One for the antenna & one for the scanner.
The main choices for antennas are a Discone.
Something like this, or similar.
Or a amateur radio dual band collinear, often called a white stick.
Which looks similar to this.
Personally I would say avoid anything which varies too much from the above & anything other than a discone which is for receive only is often a poor antenna, as it does not have to say where it works or how well it works.
A good choice for a plug & play option is a Nomad. It is not as good as some options, but it will hang in a loft, mount out doors if you want or hang in a window or a corner.
I have some home made variations of the Nomad & they are good antennas. But avoid the pre amp, as they are far from helpful to may people & can add in problems.
Total cost for the above is £22 & it can make a great portable option for when out & about where you want more than a small whip. http://www.spectrumcomms.co.uk/Aerials.htm