{{Hugs}} that's quite a common thought for Drs who don't maybe only know the basics of infant reflux. My paed tried that on with me when DS was a baby so I really laid it out about how his sleep was being effected and how much pain he was in during feeds.
So, at that strength he isn't even having 2mg per kg dose so he is nowhere near the top dose for his weight. My two needed the full 4mg per kg dose for it to be effective. Have you thought about trying a reflux formula? It may be worth a try, SMA do a stay down formula or the Enfamil AR we used you can get from pharmacies (it may need to be ordered and you can buy it but is available on prescription).
Here is a link to a site in New Zealand that is for reflux, if you click on the bit that says "by clicking here, you agree to the terms and conditions above...." it takes you to a dosage chart for ranitadine which you could print off and take to your Dr to ask about the dose. It's not a UK site but the dosing regime is the same for the UK.
http://cryingoverspiltmilk.co.nz/medicaltreatment/dosageschedule/?wpmp_switcher=desktop.
The other thing you can do is to insist your Dr refers you to a paediatrician if he is unable to help more. My Dr would only prescribe gaviscon so we had to see a paed for ranitidine and the formula.
Laura