I suspect that a nursery may be lowest cost option, though may not be best type of childcare... depending on your view of nurseries (some nurseries are far better than others).
Is the £278 per week for both children? If so, it's £3.48 an hour per child - based on each child doing 40 hours a week. It seems low to me but then I'm in the South East where childcare charges can be higher than elsewhere. Is the £278 also taking into account the Educational Funding (for your 4 year old) and does it include any sibling discount? Does it include or exclude things like nappies/wipes, also food charges?
If you want to compare different forms of childcare on cost alone, then for each category of childcare you need to determine the TOTAL cost involved over say a 1 year period, rather than just take the per-hour fee. It may also be worth factoring in something for Hassle - such as taking children to, collecting children from the childcare provider.
Make a list of pros and cons for each form of childcare, that will help you compare them not just on financial grounds. For example, a pro of a childminder of nanny is that they will take your children to the park. A nursery on the other hand will often confine the child to a room and let them out into a small area a couple of times a day.
A nanny I expect will cost you a lot more money than either a Childminder or a Nursery but you don't need to even get the children out of bed in the morning, yet alone fed, clothed, bags packed with all the spare clothing, nappies and whatever else the children are taking with them.
Also consider what happens in a year's time... when your oldest is at school? Not all nurseries operate a before and after-school club, or holiday club (or inset day club, or school heating breakdown club ). Also consider sickness... the children's sickness and also the childcare providers sickness.
Lots of things to consider. So my advice is find out about all the forms of childcare available and make a list of the pros and cons, as well as financial information so that you build a bigger picture of what will suit your family now and in the future.