I don’t think this is an NHS vs private situation. It is really hard to get accepted onto a phase 1 trial (trial investigating drug in early stage of development- usually reserved for patients who have exhausted standard treatment). This is not only because you need to be super fit, but they are also very strict on the cancer types they will take - the cancer may need to have a certain genetic signature. Each trial may only take a handful of patients. They often need multiple visits for blood tests and reviews- far more frequent than standard chemo.
What happens where I work is if they think a patient is fit enough (normal bloods, good functional status) they ask the closest unit first. If they have nothing suitable in their portfolio, they approach units further away.
You have to remember that the chance of this type of treatment working is low and this needs to be balanced against the potential side effects and the impact of the trial schedule on their day to day life. It's not ideal to treat patients who live miles and miles from the unit in case of medical problems.
I wouldn't be surprised if Lizzi's team referred her to one unit, but were told she wouldn't be suitable because of her heart issue. It sounds like she then asked for a referral to the Marsden. Fingers crossed the drug works for her (every wonder drug has to start somewhere) and all the time in the car is worth it. Lizzi we're rooting for you!