You'll find commentary elsewhere on how people value the cost of Avios. Most people seem to put them at 1p or perhaps a little less.

One way on Avios from LHR to NCL would be 2250 Avios estimated value £22.50, plus £15 tax if you are able to secure a RFS. So £37.50 using Avios vs £60 full cash.

However bear in mind that if you use Avios for the last leg you then the Avios leg would be a separate ticket. If your incoming flight is late and you miss your connecting Avios flight then theoretically you lose the Avios flight miles and cash and would have to buy a new ticket. BA might take pity on you if your incoming flight is BA as well as the LHR-NCL and put you on a later flight but if you're on separate tickets they don't have to.

If you check other Oneworld airlines that could sell you the ticket all the way through to Newcastle you might find a cheaper alternative. Depending on where you need to go Edinburgh Glasgow, Leeds Bradford (LBA) or Manchester could be alternatives that would give you a wider choice of airlines from your starting point. If you really need Newcastle then there are some nice connections from places like Brussels instead of Heathrow but these may not be on Oneworld airlines so you would lose the chance of collecting Avios.