Presumably the delay to the works would be a compensation event e.g. you were not given access to the works by the access date stated in contract data (clause 60.1(12)). If that is the case then you get to assess the full effects of that compensation event upon the remaining works. If you know there will be increased costs for any reason then these can all be claimed for within that compensation event.
If however the who project is being delayed before you have even started then this should be agreed as part of the negotiations before the contract is signed. This should be agreeing revised starting/completion date and also verifying that the tender price is still relevant to the revised project you are about to sign up to.
X1 is to cover change in inflation as the project progresses for all costs, not just compensation events.