There seem to be two areas which give the practical classic car owner the willies : electrics are the most obvious; and running a close second are brake servos. I think the problem in both cases is that you can't actually see what is going on! So here is a quick visit to brake servos.
Up to chassis number B382001284 Tigers had the small chamber (approx. 5 1/2" diameter) MkIIA servo which had a 2:1 boost ratio. This was replaced from B382001285 by the large chamber (7" diameter) MkIIA with a 23/4:1 boost ratio. The MkIIA servos are the ones with the end plate held on by either seven or eight small bolts and with the vacuum pipe connected to a union on top of the cast aluminium body. The later MkIIB was introduced after Tigers had finished production so was never original equipment (although Girling did recommend it as a replacement for worn out MkIIA's). The MkIIB has a clamp band around the vacuum chamber and the vacuum pipe connected directly to the vacuum chamber. There are also some internal differences.
No or weak servo action (in other words, a heavy pedal)
Usually caused by someone fitting a length of heater hose instead of the proper vacuum hose: this is more prone to internal collapse which stops the engine sucking the air out of the servo.
Other possible causes are loose connections at either end of the vacuum pipe; a blocked air inlet (under the filter) or a clogged filter itself. Also possible (but not that likely) is a serious internal fault such as failure of the output piston, jamming of the control piston or air valves or seizure of the air piston.
Brakes "hanging on"
Ususally only happens after the unit has been reconditioned and Girling say this is usually due to misalignment of th vacuum piston. If you examine the unit carefully you will se that the piston rod and vacuum chamber are both quite accurately located by the plastic spacer and guide bush. As this is the last part to be fitted into the main bore, any misalignment should only be due to the vacuum chamber being distorted.
It is much more likely that the air piston is sticking due to a swollen or excessively firm foam backing ring behind the leather piston seat, or the use of non-Lucas-Girling kits which don't contain any leather lubricant. There have been considerable variations in the resilience of the foam rings both in non-Girling and genuine kits. Hanging on can also be caused by misalignment of the air valves, but provided these are free they should self-align quite happily.
Brake pedal going to the floor gradually (or indeed quickly!)
This obviously means a leak somewhere, but the question is usually Where?
Callipers hardly ever leak, and when they do it's pretty obvious. The same goes for the flexible hoses (don't forget the one over the back axle) but stone damage is always a possibility. The solid brake pipes connected to the inner ends of the front flexibles are prone to rock damage and can easily fracture. Copper brake pipes are prone to vibration fatigue unless extra supports are added, so they could crack and leak on any long run.
The rear slave cylinders are the usual location for leaks and probably the first place to check but the master cylinder is also a source of leaks and it's worth checking for brake fluid behind the carpet in the driver's footwell. The master cylinder is also to blame if your foot is creaping to the floor but the fluid level is not dropping. In this case it's the small seal that closes the return feed to the reservioir which is to blame.
If the fluid level is going down and you’re absolutely sure there are no leaks anywhere then it looks at last as though your servo is leaking internally. After topping up the master cylinder for several days you will eventually lay a smoke screen James Bond would have been proud of as the fluid reaches a level in the vacuum chamber high enough for some to be sucked into the inlet manifold and burnt. It's quite spectacular! The smoke is quite characteristic - dense white which can't be mistaken for oil smoke. If you remove the servo and shake it you'll hear all the fluid sloshing about inside the vacuum chamber.
What to do with a duff servo?
Bypassing it is legal but will fail the MOT. If a servo is fitted it must be working - I don't know anyone who'd want to drive a Tiger with no servo anyway!
Replacing it with a new unit is not possible as Lucas-Girling no longer manufacture in-line hydraulic servos. You could try to squeeze a Lockheed unit in but I don't know if there's enough room to do that.
Picking up a unit from a scrap yard or auto-jumble is fraught with danger as it could be no better (or even worse) than your old unit. Picking up a newer MkIIB won't be much better as these are mostly quite old too, and if they have internal leaks they cost a lot more to recondition. They don't, however, suffer from the dreaded "hanging-on".
Reconditioning your own servo with a kit is a fun way to spend a day - be warned that you need a moderately long-nosed pair of fine internal circlip pliers and a foot of 1/8" steel wire to bend into a special tool. Genuine Lucas-Girling kits can be hard to find - alternative kits usually have no instructions and no leather grease. I have also found cases where genuine kits have contained the wrong parts - parts which appear to fit but leave you with internal leaks!
So after all this negativity, your best bet is to find a nice chap who offers re-conditioned servos