Possibly, but as a minimum you will need a charge point that has integrated open PEN fault protection, plus DC tolerant earth leakage protection, and you will need to ensure that the RCD feeding the charge point circuit is a Type A, and not a Type AC, and that there are not two RCDs in series without some form of selectivity.
The installer will do a survey as a part of the job, so will assess whether there is enough spare capacity on that supply, or whether another supply needs to be run to the charge point. In general it's better to run a separate supply from the meter tails, rather than take the supply from the main house CU, because charge points run for hours on end, and thus tend to heat up the MCB feeding them. There is also a possible selectivity issue with RCDs, as the feed from the CU (if using that approach) must come from a non-RCD protected way if there is another RCD downstream from it, or some other means must be used to provide RCD selectivity. Your installer should sort all this for you, just explain that you would prefer to have no outside cabling visible, if at all possible.
The installer will do a survey as a part of the job, so will assess whether there is enough spare capacity on that supply, or whether another supply needs to be run to the charge point. In general it's better to run a separate supply from the meter tails, rather than take the supply from the main house CU, because charge points run for hours on end, and thus tend to heat up the MCB feeding them. There is also a possible selectivity issue with RCDs, as the feed from the CU (if using that approach) must come from a non-RCD protected way if there is another RCD downstream from it, or some other means must be used to provide RCD selectivity. Your installer should sort all this for you, just explain that you would prefer to have no outside cabling visible, if at all possible.