In the original situation we would say 'traffic is a (type) on base leg, takeoff at your discretion' thus leaving it to the departing pilot to decide if they can enter the runway and commence takeoff before the traffic on base leg makes the decision to go around.
If the departure is then slow in commencing takeoff, the landing aircraft must be given 'quality' information to enable the pilot to decide whether to continue and land or whether to initiate a go - around.
Edit to add: Qwikstop: a FISO in the UK will NOT say 'runway is free for landing' but an A/G operator MAY say 'runway is clear'.