There are a few things to consider. There's the tax issue, which means you can give away £3000 per year before tax implications kick in (although, from memory, I think a person can give away as much as they like as long as each gift doesn't exceed £250).
As far as the OPG, the gifts need to be 'proportionate', so the wealthier the person the bigger the sums allowed and, as Grannie G says, previous gifting habits are also take into account.
Lastly, if care funding is an issue or is likely to be an issue, there is the LA to consider. If the gifts have been substantial and have depleted available assets, they might have something to say. But I imagine the sums really would have to be large, and I can't see them chasing a few hundred pounds given to kids, if that's the sort of thing you're thinking of doing.
P.S. I've given my sons quite substantial sums from their granny for university fees. Although amounts that large hadn't been involved previously, she'd always been very generous with them and had intended to help in this way at this time. Given the amounts (into thousands for the two of them over the period), I cleared it with the OPG before going ahead and they were absolutely fine about it.