In England people pay a small amount (£8.05) for each item on a prescription. One prescription is almost always a single month. Thus, if you have 5 or so meds on a script you'll be paying £40 per month for meds.

There is help for prescription costs - people can get deductions for long term meds.

Luckily, most people do not pay prescription cost. About 80% of people on a prescription have some exemption or other.

There are big problems with medication non-compliance, even for serious life-critical meds (cancer meds; HIV meds; transplant surgery meds) but it seems the cost (free or high cost) is not relevant - non-compliance is similar in the UK and in the US.

There are some problems with the English NHS, but "getting access to meds" is not one of them. Unless you count fantastically expensive new cancer meds that add maybe a week of poor quality life.