Changing the rear wheel offset to allow space for freewheel I've had some new wheels built for a steel frame with a 126mm rear dropout spacing. The rear hub takes a 7 speed screw-on freewheel. At the moment the rim sits perfectly central to the chainstays when the axle is pushed to the back of the horizontal dropouts on both sides. However, I've discovered that there isn't enough room for the chain on the highest (14 tooth) gear because it is too close to the chainstays.

What would be the consequence of adjusting the wheel away from the frame on the drive side (about 3mm should do it) by adding washers on the drive side and removing them on the opposite side of the axle?

Could offsetting the wheel in this way affect braking? Is it likely to be detrimental to the chainline? Would it be advisable to use adjustment screws in the dropouts to make sure the front edge of the rear rim continues to be centred between the chainstays?

Any advice would be much appreciated!
Random interference with the chainstays/seatstays/dropouts like this just happens sometimes. It's not really anyone's fault.

If you added 3mm of spacer to the drive side and took 3mm away from the non-drive side, the wheel will be out of dish. That's fixable, at the expense of increasing the left-to-right spoke tension disparity, creating less total tension and a weaker wheel. (A nice new handbuilt wheel with a modern rim will already have the drive-side spokes at the highest tension the rim can take without risking cracking at the spoke holes, so the only place you can go here is reducing tension on the left side, so less total tension). The chainline will be affected but it's not likely to matter. You'll also have increased the unsupported span of drive-side axle, which is already borderline too much for some riders on 7-speed freewheel hubs, although that depends on you and your style. 

Adding an equal amount of spacer on both sides, putting in a longer axle, and spreading the frame is likely a better approach then re-dishing the wheel. It negates all of the above downsides other than the unsupported axle part. It's always technically possible for bad things to happen as a result of spreading the frame, but for the most part this fear is an invention of people who aren't aware of the level of cold-setting punishment steel bikes receive when they're built. In actual practice, steel frames can be spread and aligned with almost total impunity.

A lot of nice 7-speed freewheels were made with 12-tooth small cogs. If that bought you the clearance you need and you could also get the gearing you need, that route sounds like the best one to me. It does mean being reliant on vintage drivetrain parts, which isn't ideal, but old freewheel cogs kind of last forever anyway so I wouldn't sweat it here.

Crimping/indenting the stay can also be a totally reasonable solution depending on what part of it is interfering and how much you'd need to do it by. Many, many bikes are made with partially flattened stays to help with clearance.