No you'll be fine. The two in the taillights must work, and the third (optional) should be maintained all brake lights together must be over 50% operational.
If in doubt remove it and take it without the high level brake and no problems.
Source Pistonheads
https://www.pistonheads.com/gassing/topic.asp?t=1099955"Road Vehicles Lighting Regs 1989 requires upkeep of brake stop lamps:
Maintenance of lamps, reflectors, rear markings and devices
23.—(1) No person shall use, or cause or permit to be used, on a road a vehicle unless every lamp, reflector, rear marking and device to which this paragraph applies is in good working order and, in the case of a lamp, clean.
(2) (b)every–
(i)stop lamp,
(3) Paragraph (2) does not apply to–
(c)a defective lamp, reflector, dim-dip device or headlamp levelling device on a vehicle in use on a road between sunrise and sunset, if any such lamp, reflector or device became defective during the journey which is in progress or if arrangements have been made to remedy the defect with all reasonable expedition
BUT
the requirement in relation to number required states
SCHEDULE 12
PART I
Requirements relating to obligatory stop lamps and to optional stop lamps to the extent specified in part ii
1. Number– Two (one if pre 1971)
it then goes on to say additionals may be fitted
PART II Requirements relating to optional stop lamps
(c) in the case of a stop lamp fitted to a motor vehicle not being a motor bicycle, first used on or after 1st April 1991 either centrally or in such a manner as to project light through the rear window the intensity of the light emitted to the rear of the vehicle shall be not less than 20 candelas and not more than 60 candelas when measured from directly behind the centre of the lamp in a direction parallel to the longitudinal axis of the vehicle.
So it seems that Reg 23 is specific in that, despite law only requires two lamps and extra are optional, those fitted have to be maintained otherwise offence.
Bearing in mind MOT does not allow unlawful items then I would presume any extra not working gives grounds for MOT refusal.
This is backed up by the fact that the MOT Testers Manual state in relation to Stop lamps:
This inspection applies to all stop lamps fitted and gives the reason for a rejection as:
Inoperative or less than 50% of the light sources illuminating."
