Don't blame the political masters, at least not for this one. It is an own goal by the Army and RAF high paid help. As is often the case, the Navy are ahead of the power curve and actually encourage their servicemen and women to be seen in uniform in public. I bet it does great things for their self-respect and for recruiting.
The security rationale for creeping around like grey mice is frankly b*ll*cks. Even when there was a real IRA threat it was counter productive. When I was serving I hated having to disguise myself as a civvy, totally ineffectually as we all came and went from our place of work in full view, short haircuts, lean and mean appearance (I was much younger then!) and carrying a military duffle bag died red or blue or whatever. Didn't do much for our morale and self esteem but must have been great for the opposition to see they had us on the run. We are British soldiers. We should flaunt it proudly.