Yes you can get one that will do freeview, dvd-r and hd-r but i doubt you will find one for your budget.
My recommendation would be the Humax 9200, although a little over your budget, is a brilliant box. It has dual tuners so you can record and watch different programs. As long as you leae it on the correct channel, you can actually record 2 channels at the same time, if you go out or something. Signal quality is good, picture quality is good.
It has optical out for when terrestrial channels support Dolby Digital, A large enough hard drive for a lot of recording.
If you really have to stick to your budget there is the Humax 8000 which only has one tuner, but is still a good box.