You are right about IRR being applicable. That being so the building owner should be able to provide you with their 'Local Rules' for working in the area - these will vary depending on the assessed level of exposure, and have to be approved by their appointed Radiation Protection Advisor (RPA).

My guess would be that they havn't actually done any of that and are covering their backsides! Simple technology is available to measure the amount of radon present, but it takes a while to do this at the typical low levels experienced in those areas of UK where this hazard is present.

If they do have Local Rules, then there needs to be a competent Radiation Protection Supervisor (RPS) in charge of the work, ensuring that it's all carried out in accordance with the Rules. Pretty obviously, you can't quote for the work until you've had sight of the Local Rules!

They know there is Radon gas present. Therefore someone has done some measuring. If someone has done some measuring they should have a rough idea of the levels.

Most buildings with Radon in them have some sort of ventilation system to prevent it building up in the basement. Would be my first move; either improved natural ventilation, or forced ventilation.

As mentioned by imwaldra and Descarte8 the IRR does apply. When it comes to natural sources of radiation, the guidance suggests (Paras 11 and 13 plus bits of Reg 3 and 6) it would only be considered a problem if the doses received by the operators approached 1mSv.

Either way I would still ventilate the area thoroughly, and ask whoever did the original measurements to re-measure until levels are approaching MDA (Sorry! Minimum Detectable Activity - as low as the detector will measure) and then there shouldn't be any need for restricting working times.

HTH
Andrew