First, we need to clarify what "non-human" insulin you are talking about. I initially thought you meant animal-source insulin, but finding a recent news story about the NHS's concern, it appears your concern is with the recently-developed insulin analogs.
In any case, my view is entirely different than what you have read: "human" insulin is not an inferior form of insulin, and all forms of insulins are associated with possible weight gain.
First, for clarity so we are on the same wavelength on one point: what is frequently called "human" insulin does not come from human beings, but instead can be manufactured in such a way as to precisely mimic human insulin. The manufacturing technology is called "recombinant DNA" technology, and is now used for almost all insulin production, as well as the production of many other hormones and proteins. This is a completely different way of obtaining insulin than when obtaining bovine (cow) or porcine (pig) insulin, which is extracted from the pancreases of these animals (which are obtained from slaughterhouses when the animals are processed for meat and other products).
An additional point, which the NHS is concerned about: insulin manufacturers have now developed variants of human insulin that are not precisely the same as human insulin, which are called insulin analogs (or analog insulins, if you prefer). These analogs have a few amino acids that are different from human insulin, and hence have different characteristics: some (including Humalog and Novolog and Apidra) act more rapidly than human insulin, and some (including Lantus and Levemir) persist much longer than normal human insulin. There has been some concern that analog insulins might be associated with cancers, and indeed one ill-fated insulin analog [AspB10] was found to induce breast cancer in rats. There also was some concern a few years back that Lantus might be associated with an increased risk of malignancies, although regulatory authorities were not impressed, and the American Diabetes Association thought the studies "conflicting and confusing" and "inconclusive." These insulin analogs are indeed more expensive than the earlier versions of human insulin.
You are correct on your last
comment, but ascribing the problem of increased storage of fat to human insulin alone is wrong: any insulin can cause weight gain if excessive calories are eaten. Why? Because insulin can be viewed as a "storage hormone:" it works to store glucose as fat. If anyone overeats while on insulin therapy, and adjusts the insulin dose to keep the blood glucose levels near-normal, and doesn't increase their exercise levels dramatically, the result will be weight gain. Believe me, I've seen it in patients on insulin therapy for many years, including long before human insulin was first commercially available in 1983.