Could be a VMO tear??? The VMO is mainly active towards full extension of the knee and not really used too much during walking. If stairs/ cycling/ fully straightening the knee are very painful it is at least possible.
These things are very hard to describe and judge even for your Doctor. If you have damaged a ligament then the GP should be able to pick this up by pulling your knee bout (technical description).
The only way to tell for sure if you have any other soft tissue damage is to have an MRI although your GP will be very loathed to give you one as they are very expensive. If there is some soft tissue damage then chances are that by the time you actually get an MRI it might not be the best timing.
On the other hand, it might just be something minor and one of those annoying niggles which goes away quickly hence why a GP will not be rushing the expensive MRI unless something really jumps out to them. Most likely you will get ibuprofen and be told to rest for 6 weeks.
For the time being, I think the only advice a Doc would give you is to only do as much of anything as you are comfortable with. Bracing is most likely OTT, especially until you see the Doctor tomorrow.
GP is the only route to any form of investigation or treatment so it all depends on your persistance/ symptoms really.
Oh and yes, I am very cynical of the NHS mechanisms for sorting knee injuries but can fully appreciate why everything is as it is