Does the fight scene involve weapons? That will make it expensive to shoot anywhere. And you'll have to pay for a permit at any public location if you're using a crew (including cast) of more than 5.
Also, day or night? Interior or exterior? Street or park? Central or suburban?...etc.
Any striking location which is free in London and accessible. 'Free' meaning 'no money' and 'accessible' meaning I don't have to, for example, break into the Bank of England.
Do you know any free ones? My last short was shot in almost entirely free locations.
A boxing club, inside a work of art (how crazy was that...???), on a bridge in front of a waterfall etc... Hell, I was told it was 'impossible' to find a free location with a waterfall in London. So I got hold of a location, free of charge with the permission from the management company that charges professional outfits £5,500 to shoot in the identical location. In fact, it was the same site where a chunk of Bridget Jones' diary and a Jude Law film were shot.
I had an entire racetrack, a race spec motorbike etc...
And I wanted a stunning location for one sequence with a view of St Paul's, the Thames, the Gherkin, the Globe and I had that as well.
The trick is finding the extremely striking location which is free and accessible. After this, the other details will take care of themselves.
So I will ask... does anyone out there know one in London?