It really depends on where the fibroid is - is it in your actual womb or the walls/outside the womb? If it is actually in the uterine cavity (sub-mucosal fibroid), then at 6cm it should be removed as it is very likely to interfere with implantation. I don't want to scare you but this type of fibroid can also cause issues during pregnancy such as late miscarriage/pre-term labour, so it really is better to have it out before becoming pregnant.
If it is in the walls or outside the womb then it is likely fine - I had three fibroids pre-pregnancy and was told repeatedly by various consultants that they would pose no threat to conception because of their location. Two were in the walls and the largest was outside the womb.
I would really recommend finding out exactly where the fibroid is located before making any decision regarding fertility treatment. Even if you have your treatment abroad it is a lot of money to spend if your chances of the IVF working are reduced by the presence of the fibroid. Ironically sub-mucosal fibroids, whilst the most challenging of all the fibroid types to fertility, are the easiest to remove via laparoscopy or hysteroscopy.
I have no experience of this myself as had IVF treatment in the UK, but I believe some foreign clinics offer a hysteroscopy before commencing IVF treatment, so if the fibroid does prove to be an issue you could always discuss having it removed first and no doubt this would be much cheaper than having it done in the UK (since you say the NHS won't do this).
If it offers you any hope IVF has an excellent chance of working even with multiple fibroids - the largest of my three fibroids was 5 cm before starting IVF and I am now 34 weeks along. I had IVF at the Oxford Fertility Unit (NHS-funded) and luckily our first round worked. Previously we had three years of unexplained infertility with just one very early miscarriage/chemical pregnancy.