Yes you can get pop in breaker replacements.
They look something like this: 
The important thing is to ensure that you use a breaker that is the same ampage as your fuse (or very close to). When I did mine (before rewiring the house) I had some fuse wire that was something like 15A. But the closest breaker was 16A. That's usually ok because the wiring is actually rated higher than that. But for safety make it as close as you can.
Breakers on ebay in UK...
Three Phase Power
In three phase systems, there are three "hot" lines (L1, L2, L3). Often there will also be a neutral (N) and a ground (G). The neutral and ground should be bonded together at your service entry). The three lines are all 120 degrees apart from each other. Loads can be attached in either a wye or a delta configuration. In residential applications, often only two of the three phases are supplied (and different houses will get different pairs of phases as to balance them).
Delta
In a delta configuration, loads are attached between phases (and a neutral is not needed). This configuration is common for large motors and in industrial settings. In some delta configurations, a terminal on the transformer's secondary is grounded and provides a neutral. The ground terminal would be either one of the three lines or a center tap on the coil between two lines (creating a high-leg delta configuration since one of the lines is at a much higher potential (with respect to ground) than the other two).
Wye
In a wye configuration, loads are connected between a line and the neutral. Based on the question, I believe that this is the configuration being used. The power company supplies the three phases and a neutral, and the customer supplies the ground. Normally, the neutral is connected to the ground (which is bonded to metal rods in the earth, water pipes, etc...). If the load is properly balanced (meaning that there are equal currents flowing on each phase), the neutral currents will cancel out to be zero and the neutral would be unused.
However, it is rare that the three lines will be exactly balanced, so there would be a neutral current flowing based on differences of currents in the three phases.
The Root Cause
My hypothesis is that the neutral in the building is not properly connected to the power company's transformer. Without a good neutral connection, the neutral voltage is not held to earth potential (the ground connection usually has 1-20 ohms resistance to the earth). The neutral voltage will drift towards whichever line is the most loaded (as it forms a voltage divider). For example, if L1 has a large load and L2/L3 are lightly loaded, the neutral voltage will be pulled towards L1, causing the L2-N and L3-N voltages to became much larger than their nominal voltage.
So, the fix would be to repair the neutral connection between the building's breaker panel and the power company's transformer. This may be a bad connection of the neutral in the breaker panel, or a failing transformer. Repairing this could be dangerous because the problem might be in a section of cable that cannot be easily turned off (if the break is before the building's main breaker). Working with the power company to turn off your service or check their transformer will likely be needed.
Split-phase Systems
This problem has an analogue in the split-phase system which is common in the United States, and there are related questions on this site:
Best Answer
No, there will not be any extra regulatory hoops.
As to materials cost a three phase DB will cost more than a single phase one but the cable is likely to work out cheaper. Overall I would expect for a given power level a three phase feed to work out cheaper than a single phase one.
Don't expect this to be a cheap job, mostly because you are going to need a long peice of fat cable. Using aluminium cable is an option to lower the cable costs but it can be difficult to find electricians who know how to work with it safely.
Any electrican who regually does commercial work will know how to deal with three phase.
As long as the structure is sturdy, weathertight and reasonablly permanent the fact it's timber shouldn't be a problem.
The job will be notifiable under "Part P" because new circuits are involved but nearly all electricans will be part of self-certification schemes so that should be a non-issue.