People always say this, but there's a lot more nuance to it. For example, the power price goes up and down throughout the day, but the price generators pay for gas doesn't change half-hourly. The efficiency of gas generators varies considerably, so only the most efficient gas generators will be in use when there is a lot of renewable generation and the price will be much lower as a result. It was £-5/MWh earlier, so gas generators were making a loss at the time.
The amount of renewables are also driven long term by other factors which affect the generation available and therefore the price.
It is true, however, that higher gas prices will raise the prices for the same level of generation by other technologies. It also encourages investment in renewables which, if successful, brings down the price, which discourages investment in renewables, etc.