If you’re not going to be registered with Ofsted then the definitions are not particularly well-defined. Ofsted (very loosely) consider "babysitting" to be an ad hoc evening activity.
You could advertise as a babysitter but I suspect parents responding to such an ad would be expecting an evening service.
Definition-wise, it sounds more like you’re offering an occasional nannying service.
You can register as a nanny with Ofsted, or operate as an unregistered nanny, in which case you need to check Ofsted’s rules on "no requirement to register" to remain legal. This broadly means working in the parental home rather than your own; or in your home for less than two hours maximum.
There’s a MNer called NannyNick who can give excellent advice on this.
Tbf, you should be very honest with parents about some of the limitations. Unless you charge rock-bottom fees, they’d be better using a registered childare provider who they can pay through money-saving schemes like childcare vouchers tax free childcare. There could also be issues over insurance and responsibility in the case of an accident. You may need to use much more expensive car insurance if you intend to drive the children, or even to just drive yourself to/from their homes.
It might be viable, but worth getting everything right, which could prove expensive.