Yes, you can, as long as it's all on BA. It costs no extra avios to connect to other UK cities on domestic flights, but for all other destinations you will pay avios for each leg of the journey.

Also, be aware that BA adds hefty fuel surcharges to award tickets. If you are planning to fly economy, BA awards may not be a good deal, but if you are planning to fly business or first, you can get great seats for a fraction of the usual price.