To respond to the initial questions, Yes it is possible to find nannies who live out. Cost will vary a bit depending on area, though budget for around £10 per hour and you won't be that far out. As a daily nanny (live out), I cost my employer around £10 per hour, thus as I do a 10 hour day, cost is £100 a day. For my employer this is cheaper than a nursery, as there are 3 children involved soon to become 4.
The arrangement is as reliable as the person whom you hire. One drawback of a nanny is that if the nanny is really ill, then there is no backup. However, nannies tend to work if a little under the weather (though obviously not if infectious), and as a nanny I can say that I've had no days off due to illness in the past year.
There are other costs to consider when comparing a nanny against other forms of care, for example the weekly budget for expenses. This will vary depending on cost of social activities in your area and what you want the children to do. Personally I tend to spend around £20 a week on activities - such as music group, swimming (one of the bigger budget eaters), toddler group, and other outing associated costs. Also if your nanny is providing their own transport, you need to compensate for that in some why, typically by paying an agreed mileage rate, or fuel allowance.
As others have already mentioned, costs at home will also increase a bit, as there will be more use of facilities during the day. However there are also advantages to this, such as household tasks being done, having more control over what your children eat, and having an employee who works the hours you require (by prior arrangement), to name a few.
I reckon that with two children, with nursery costing £1600 a month, that a nanny will probably work out a bit more expensive, probably closer to £2000 a month if nanny works say 50 hours per week. However you need to weigh up the pros and cons of both forms of childcare and see which your childrens needs and your own.