First of all, patience and an eye for the long haul may be required. The starting cargo numbers are low and the economy builds fairly slowly. The economic engine is coal-fired, just like your locomotives.
In the beginning, build a railway rather than investing in industry. Liverpool-Manchester-Birmingham is a good starting area, but others (Bristol, London) may work well for you. Get started hauling cotton to the mills and clothes to the cities and docks. Once the annual coal haul comes up over 25 or so, build or buy up industries as they will be running at normal or above. Hotels, restaurants and taverns are profitable.
Once you begin laying track you must pick a gauge. Broad gauge is more expensive to lay (40%) and much faster (25% plus 1 acceleration level); standard gauge gives ordinary cost and performance. Track maintenance is HIGH and WILL GET HIGHER but is the same for broad and standard track. Make sure your routes earn a profit! You must maximize revenue and minimize expense or the rising costs (and tax) will eat you up.
First goal is to connect 45 cities by August of 1846. Parliament will make broad or standard the law of the land, and you will win if you control the votes, so 45 cities must be connected with YOUR stations. If you can get more than one city in the footprint of a station, they all get counted! So build, build, build! You will make a lot of money in the early years. I usually win the Gauge War by 1842 to 1844.
From 1842 to 1844 it gets harder. Parliament re-imposes the income tax and begins exerting more control over the railways. One law requires your average annual express speed to be 12 mph or faster. If you fall below this you will be fined $50,000 every month until you fix the problem. Double-track your bottlenecks, improve bridges, upgrade to faster locos or (last resort) use priority PAX trains. I have used two stations for Birmingham and two for London to cut down on the congestion.
In 1851 the Great Exhibition will give you a large passenger surge. After that passenger production (and prices) begin to fall. This reduces the otherwise-huge cash glut and frees up cars for freight, which is what you win the game with. Better locos pulling more cars (like Firefly and Crampton) will give your annual hauling totals a boost.
Buy your way into Scotland and buy or develop the industries there. Edinburgh-Glasgow-Ayr and Edinburgh to Aberdeen are profitable routes. Connecting Edinburgh to London takes time and money, but it is pretty straightforward. Whether or not you should build in Ireland is determined by the raw material available there. Buying in is fairly cheap (like access to Scotland) and the railways are easy to lay. Industry in Ireland can turn a good profit and any loads you haul will count. So don't overlook Ireland! :)
Take every opportunity to increase your textile output. Once 1848 rolls around you can begin weapons and ammunition production. 1856 means Bessemer steel arrives. Britain will have A LOT of textile mills and tool and die shops; get as many of them working as possible. I rarely have a time when clothes and goods aren't profitable to haul.
AVOID letting textiles, goods, weapons and ammo be manufactured in a city that has a port or warehouse that demands them! You want to HAUL these, remember!
You will be offered a chance to pay for dock improvements. This costs a lot ($10 million up front or $120,000 per month for ten years) but markedly improves your imports, especially iron.
The Crimean War in the 1850's will boost weapons and ammo prices. There is a bank crash in 1857 that gives a Depression, and the American Civil War arrives in 1861 to shut off cotton imports (look for wool and don't panic; as clothes get scarcer they get more expensive and they travel more :P ).
There aren't any real tricks to this one - certainly no government bonds or land sales :) - just straight-ahead steaming. Building the economy does take patience and ruthless expansion of rail net and industry alike. Above all else, be profitable and efficient - track maintenance costs can be brutal!
Once the coal, clothing and goods haulage victory conditions for Silver are ALL met you will qualify to work on Gold. Hauling 1000 coal, 1000 clothes and 500 goods each earns you one point. When you have those three points you can begin to add points for Gold; three points is a Silver and eight points is a Gold victory.
Bronze:
Connect London to Edinburgh by 1870
Silver:
Connect London to Edinburgh
Haul 1000 coal, 1000 clothing, 500 goods by 1870
Gold:
Win the Battle of the Gauges
Connect London to Edinburgh
Haul 2000 Coal, 2000 Clothing, 1000 Goods, 50 Weapons and 50 Ammo
I hope you enjoy the game. Thank you to wolverine and bombardiep for their advice and patient play-testing; the things you like about this one are probably the result of their labor. Any errors are, of course, mine.