The lake I intend to fish has a ban on floating baits, including flys. So, the obvious method of using a Deer Hair mixer imitation is a non-starter.

Could anyone suggest a viable alternative method? I intend to fish on warm days when the fish are near the surface. An inch or 2 under the surface is fine, but floating is not. So what flys might I try, how would I keep them in the surface layers?

Thanks in advance.

try a slow intermediate line with a super slow sinking leader whychwood make them. Count down according to leader weight and fish there in.
Flies i have used to great effect yesterday were bloodworm buzzers and wooly buggers using a slow retrieve.
Als ihave used bread flies made with antron body wool. sinking fly.
Or fish a team of flies on a decent leader fishing multiple depths at once hope this helps

Catching these cruising carp can be like shelling peas if you get it right. After a few years experimenting, i have settled on a couple of key points. The most important thing is not the fly itself, but the way in which it sinks and your delivery. The fly needs to sink as slow as possible, almost hanging in the first foot or so of water, maybe taking 15 or 20 seconds to sink out of sight. I now prefer flies of a largish size(normal sizes are 10 or 12 on drennan trad wet or even kamasan animal) and fairly heavily dressed and bushy.
-fritz/tailess blob in any colour really but darker is easier to spot
-palmered white wool or sheep hair tied scraggy to look like a hunk of bread
-black chenille and pearly hopper with cock hackle
No need to get hung up on patterns though because any that behaves correctly and are sizeable enough to attract the attention of a carp in muddy water will catch, but the ones I have mentioned are quick ties and easy to fine tune the sink rate by a bit of gink, or trimming or vigourous false casting.
It's as simple as arriving at the time of day when they are up and moving, casting with just enough lead so it lands at eye level and in line(must be accurate!) , and just let the fly hang, NO MOVEMENT, and you will see your fly disappear(a large and visible fly helps), or the carps mouth extend, or if he follows your fly down then watch your leader or leader/line connection like a hawk as the takes will be subtle due to the way in which carp suck in their food. My usual kit is an 8#rod and line, braid sleeve with a bit of floating putty to keep the tip up, and a level leader about 5-8foot long of something solid in 5-7lb bs, you do need the shortish leader to help with bite indication when you cannot see the fly or carp.
Fishing like this I have caught up to 50 carp in 5 or 6 hours for 100+ lb of fish, but a water I have fished a couple of times has an average of 5-8lbs with some low doubles which really make your arm ache on a single handed rod with no fighting butt! No need for loose feed with this method by the way.