Am I breaking the law by using "TM" on my trade mark?

No, as this does not indicate that your trade mark is actually registered, only that it is being used as a trade mark. The symbol "TM" has no legal significance in the United Kingdom.

Many traders place the letters TM (trade mark) or SM (service mark) against their marks. It offers no legal protection at all. If traders are placing the letters TM against a mark but have not registered that mark then others may apply to register that mark. The use of the letters TM will not affect the outcome of examination of that application but they may oppose the application once it is published. Please note that anyone may oppose a published trade mark application.

If an applicant is relying on evidence to demonstrate acquired distinctiveness then it is not the use of the letters TM that is critical but use of the words etc. as a trade mark. Please note that other factors are taken into account when considering such evidence which must demonstrate use throughout the UK.