A monetary union such as the Eurozone is the use of a single currency and the monetary control of the currency (monetary policy) is run by a central bank (The ECB - European Central Bank). Fiscal policy requirements are put in place such as member countries not having a budget deficit larger than 3% of GDP.
UK's Financial Heart
A possible benefit to the UK of monetary union is lower transaction costs. Trading between countries will become easier as there are no forex costs or fluctuations which might reduce a firms ability or willingness to trade, this is highly important to the UK as 60% of its trade involves the Euro. A single currency also means that comparative advantage is able to be further refined between member countries as it might not be fully exploited presently. In addition to this, there is a positive effect on consumer welfare as firms cannot price discriminate.
However, presently, forex charges are already being considered by UK based firms who trade with the EU. This is done by purchasing 'options' (which is future insurance against forex fluctuations) which can be effective and sometimes increase profits. Also, the 'options' which are usually purchased by both UK and EU firms are purchased through the UK financial sector. So a major income stream would be lost here which would likely worsen the current account on the balance of payments as the finance industry in the UK (service sector) helps to balance the usually negative Balance of Goods on the current account.
In addition to this, the £ has appreciated against the € recently which has provided firms and consumers with cheaper EU imports, which for firms can be used to produce cheaper exports for the world market as raw materials such as french electricity are cheaper. This benefit would be lost in a monetary union.
Finally, the UK economy's productivity is likely to be maximised when comparative advantage is at its freest rein i.e. outside of a monetary union with higher levels of protectionism.
Nissan's highly efficient UK plant
A Possible Increase in FDI
Another possible benefit for the UK of monetary union is a possible increase in the FDI from TNCs. These TNC's would look to take advantage of the UK's highly skilled human capital and productive capital stock along with its position inside the monetary union in order to have greater trade with the rest of Europe. This would also help balance the capital account on the balance of payments for the UK.
However, it could be argued that the UK has received FDI despite not being in the Monetary Union e.g. hosting Nissan's most productive factory in Europe, along with Japanese car firms in the 1980s who moved due to the UK's fairly unique combination of EFTA access and the rest of the world access, along with the £ being weaker than the € at the time against the ¥.
In addition to this, the freer trade the UK has now outside of a monetary union means UK industries may be operating more efficiently now and the FDI would simply try to fill the gap left by falling productivity of UK industries inside the monetary union.
The Monetary Policy Control Issue
Finally there is the issue of Monetary Policy Control. One benefit could be that inflation would be controlled and limited; given the UK's history of high inflation and Germany having very stringent control in recent history. This centrally controlled Monetary policy may also provide firms and consumers with high levels of confidence and therefore increase AD and LRAS
However the UK has now very low controlled inflation of circa 0% after the Monetary Policy Committee was formed in 1996 for the purpose of inflation to be kept at 2% (+/- 1%).
Importantly for the UK it would not be able adapt interest rates for its own economic needs in a Monetary union e.g. if the economy needs a boost from lower interest rates, France and Germany may not want lower rates this is because the UK is a highly consumption driven economy (60% of AD) whereas Germany is an (X-M; net exports) economy with a high marginal propensity to consume. The reverse of this is also true , that a country may need deflationary monetary policy such as the Republic of Ireland historically.
Despite this it could also be argued that the UK is a microcosm of this situation, whereby Wales, Scotland, Northern Ireland and England all have different economy structures yet the Monoetary Policy committee is able to manage all of these simultaneously.
The UK's Monetary Policy Committee
Illustration of differing short term trade cycle
In conclusion, it could be said that the UK is a strong economy independently and its structure is suited to this and more recently (2014-2015) the UK has seen low levels of unemployment (5.7%), positive growth and a reducing Balance of Payments Deficit so the joining is unnecessary.
A final larger problem would be that for currency union to work, "convergence" is needed with countries having very similar inflation, interest rates and position in the trade cycle. However a position in the trade cycle is hard to identify, the UK's budget deficit is higher than 3% of GDP (5.7%) and its economic structure is not similar enough to the core countries of France and Geramany.