In the UK, if you are offered a contract role (inside or outside IR35), accept it and you cancel the contract before the start date and if the contract doesn't mention any clauses for this, could you be sued for anything at all? (Say you get a better offer somewhere else while you were waiting for the start date of the role you've already accepted).
You can certainly be sued if you breach a contract.
However, whether you have breached your contract depends on the terms and the circumstances of the cancellation. Damages would also depend.
It might also not be clear whether this was an employment or a commercial contract - the detailed rules for tax purposes do not necessarily apply more broadly.
The general principle with employment is that you can give notice to terminate the contract. If there was no reference to termination in the contract, then it would generally be treated as an "at-will" contract until statutory requirements kick in (it would not be treated as entry into permanent servitude).
Even in a contract that is not one of employment, but requires personal service, there may still be an implied right to terminate on notice, unless the whole contract is itself for a very brief and imminent period.
Contrary also to the warnings given by @DaleM, I think the courts (at least in the UK) would be reluctant to award big-money damages if you are trading as a private individual who is only really earning a wage (rather than as an established firm which are making real profits above any individuals' wage, or have real accumulated capital). This is the difference between real businessmen and temporary workers.
The courts might award damages for the administrative cost of finding another contractor (probably a few grand tops), but in terms of the cost of that other contractor, or the consequential losses for work not done, I think they'd tend to think that there risks being wider mischief from employers engaging with wholly unsuitable "contractor" workers, and then trying to clean them out using the judicial process when something goes wrong, rather than just contracting at market rates with a suitable supplier in the first place (who offers all the guarantees and insurances of a commercial contractor taking on high-liability work).
The general principle with employment is that the employer bears commercial risk, including the costs of project failure or the drop-out of key staff (which may happen for a variety of reasons in practice).
Employers can take their own chance on employing an unreliable worker (or small trader) who is key to success, but they cannot come to court later expecting to use the legal process to shift all the cost of failure to that worker and grind him to dust - instead, the employer either has to accept the risk, or has to organise the activity to be more resilient to staff changes in the first place, or take an advance deposit from key staff (for example, by making them business partners with sunk capital).
It's for this reason, as well as the difficulty of enforcing blood out of a stone, that such cases are rarely pursued to court.
If you haven't already announced the cancellation, then the best way out would probably to induce their agreement to a cancellation, rather than simply declaring a cancellation.
The other side will surely understand that enforcing specific performance on you is impossible, so their alternatives at this stage are either to accept cancellation and look elsewhere, or to allow the contract to come into force where they are liable for a price but you might either render a perfunctory and poor-quality performance, or you might just crash out of the contract anyway (but later rather than sooner).
Yes, you could be sued
Assuming that you have a valid contract, then failing to perform your obligations is a breach and the other party can sue for damages. The damages for breach of contract are for them to be restored to the position they would have been if the contract had been completed.
If you have a contract for service
Here you are contracted to perform a particular service: build a building, write a program, cut some hair etc. you are being paid for what you produce, not for your labour.
The damages for this breach would be the expected value that they would have received. For example, if you were contracted to repair a classic car for $10,000 that they had a buyer willing to pay $100,000 for and that buyer pulled out as a result of your breach. The damages would be $100,000 they expected - $10,000 they would have paid you = $90,000 less whatever the market value of the unrepaired car is.
If you have a contract of service
This is a traditional employment contract or any contract where you are paid by the hour/day/week/year rather than for producing a specified outcome.
For an employee, there will be required notice periods that you must observe or you are liable for paying in lieu of giving notice. In the circumstances, an employer is unlikely to sue for this.
For a contractor, the damages could be the cost of finding a replacement through an agency (say $2,500) and the difference in rates - so if you were being paid $50/hour for 12 weeks of 40 hours ($24,000) and the cheapest suitable replacement is $65/hour ($31,200) then you could be held liable for the difference. Again, it is unlikely an employer will bother to sue.