If your employer is part of a larger business then you can insist on fair treatment and complain that forbidding you to cycle is unreasonable behaviour. It may even be against their green policy etc.
If your employer is a very small business (seems likely) then you have far fewer rights but if you insist on riding in they cannot sack you for it without risking facing an employement tribunal for unfair dismissal. You should mention to your boss that cycling to work is really important to you (why else would you be here!) and ask him/her to suggest a compromise as their suggestion that you give up cycling is unfair..
If your employer is part of a larger business then you can insist on fair treatment and complain that forbidding you to cycle is unreasonable behaviour. It may even be against their green policy etc.
If your employer is a very small business (seems likely) then you have far fewer rights but if you insist on riding in they cannot sack you for it without risking facing an employement tribunal for unfair dismissal. You should mention to your boss that cycling to work is really important to you (why else would you be here!) and ask him/her to suggest a compromise as their suggestion that you give up cycling is unfair..