My dentist says

You cannot even cover instrument/material costs for £40 that are required to undertake the treatment! If you value your tooth you need to give it the very best chance and invest in the best treatment you can afford.

Done well Root Canal Treatment is a complex and time consuming process requiring special instruments and expertise, however all dentists are trained to provide such treatment
To comply with his NHS contact your dentist should offer exactly the same standard of care under the NHS and Privately and if this is not the case then you may wish to take this up with your local PCT (primary Care Trust)
One option that your dentist has not offered is for you to have the treatment carried out by a specialist which is likely to cost a little more than the private treatment offered but should give an outcome which is superior to that provided by a General Dentist

Root can treatment can be a complex and important tooth saving procedure.
£40 may pay for 10 - 20 minutes while £300 may pay for about 90 minutes of professional time.You do not indicate if the £300 represents specialist a referral. If your dentist is to carry out the treatment himself ,it sounds as if he will feel more confident to obtain a good result given the time option .The result he would obtain in for example 20 minutes may be just adequate but may not meet his or your expectation.
All this in relation to the NHS is another issue altogether.

I would recommend the private option, even though you are entitled to root treatment under your NHS contract, as your dentist is likely to to take more care and do a better job if you pay him more. Root canal therapy is difficult and requires time and care to do well so it could be false economy to opt for the cheap approach. Done well you could save your tooth but if the task is rushed the treatment is likely to fail and then you will lose the tooth and the money !

The key thing is to consider the amount of time your dentist is likely to spend treating the tooth. £40 buys around 10-20 minutes worth of time at best, while £300 may buy 60-90 minutes. The more time spent the more thorough the cleaning and disinfection process, hence the greater success rate. Root treatment is the foundation to a tooth, with out a good root filling the tooth will cause problems and require either retreatment or removal.

Ask your dentist how much time the private treatment will take and make a decision from there.

Private treatment will also offer your dentist the oportunity to use the best techniques and materials while the NHS will non pay for these.

Hope this helps.