I have been told 10th April but I am on holiday the week before, which means next week would be my last week in work, plus I'm off tomorrow. However I only have a verbal offer and I've seen no contract or confirmation of day rate, if I tell the project them may invoke notice and look to replace me when I don't have a confirmed job to move into, which would be bad.if you don't want to burn bridges tell them as soon as possible then. if the other company is asking for a start date, then just give your current employer 2 weeks.