This area is one that needs lots of investigation in order to sort the facts from opinions.
Corgi have a friendly helpline, you can find the number at:-
http://www.corgi-gas-safety.com/
The Gas connection, without exception requires a qualified person to connect / work on gas.
However, gas men are not plumbers / heat engineers by trade.
The Instituate of Plumbing and Heating also have a friendly helpline, this can be found at:-
http://www.iphe.org.uk/
Unvented systems definately need qualified installation. This has nothing to do with Corgi certification.
Your local Building Officier will be wanting to hear that you have contacted the correct people. This are often quite friendly too.
Your insurance company may also require, through exemption that any / all heating / plumbing upgrades need certified installation, otherwise home insurance may not be valid.
Electrics, depending upon the location / type of connection, can also need qualified installation.
Some work can be done via DIY, but you'll have to check this with the 4/5 different parties concerned:- Corgi, IPHE, Building Officer, Electrician, Plumber.
Installers will vary. Some may be happy to validate work, others may not.
You'll need paperwork signed off - so you will also need to put this in to the mix. (Warranty, Benchmark etc).
You'll also need to use the following formula to work out which route you undertake :-
Current fuel costs minus expected cost savings with new boiler multiplied by amount of years that you intend to live in the property compared against actual official quote for installation. Take the difference, divid difference by amount of people living in house divid again by amount of years you would like to live. Consider whether the value at the end is all worth it.
Alternatively, ask British Gas to quote you for the work, then some registered fitters and be pleased at the amount of money you've managed to save!