One of my pupils came back from the holidays having improved so much that I had to ask him why? He replied that he had bought a new piano and couldn't stop playing it! Just what every piano teacher wants to hear.
I do hope that all pupils have a decent piano; it can be a digital (plug-in electric) or an acoustic(normal) one. However, playing on a keyboard, if you are learning to play the piano, is not very satisfactory as it feels different, good dynamics can't be obtained and very often there aren't enough octaves or even pedals. Progress will be slower.
If you want to buy a digital piano, Roland,Yamaha and Casio do some excellent models at varying prices. If you would like an acoustic piano, you cannot beat a Yamaha U3 but do look at others. Allegro in Chelmsford always has some secondhand pianos of all types and makes in and they are always happy to speak to customers about what would be best for them. Alternatively you may consider buying one elsewhere. Make sure all the keys and the pedals work, that it can be tuned and that it sounds good- your child will know! Extra info is available here from the piano tuners association: http://www.pianotuner.org.uk/pta221.htm