Here is a quote from the Network Rail Business Plan 2006 (Page 8 of the link below.)
http://www.networkrail.co.uk/documents/3103_Route%204%20Wessex%20Routes.pdf

"It not expected that any service enhancements are required on the line from Castle Cary to Dorchester (although journey time reductions are aspired to by local stakeholders and opportunities will be sought to achieve this in conjunction with other activity)."

Here is how SLC2 attempted to address the issue above :

F4 WESTBURY – WEYMOUTH
 
1 Route Definition

1.1 Services shall be provided between Westbury and Weymouth calling at Frome, Bruton, Castle Cary, Yeovil Pen Mill, Yetminster, Maiden Newton and Dorchester West.

1.2 Limited Stops shall be made at Thornford, Chetnole and Upwey.

1.3 Services may be joined to services specified in Route F2 (Bristol Temple Meads - Westbury) or Route F5 (Westbury – Swindon).

2 Frequency

2.1 Mondays to Fridays

(c) Between and including the Early and Late Services, eight services shall be provided at two-hourly intervals.

3 Limited Stops

3.1 Thornford and Chetnole

On Mondays to Fridays and Saturdays, one service shall call.

As we now know , this is not how it turned out in the final First Great Western Timetable. Here is a quote from the time :

"Services between Bristol Temple Meads and Weymouth will be retimed to better suit leisure and commuter customers on the line, including the retiming of a morning peak service from Frome to Bristol Temple Meads. Connections at Castle Cary to and from the West of England will be improved as a result."

Even if Westbury - Weymouth line customers had recieved a 2-hourly service , then I doubt it would have lasted for long.

Both the Merehead & Whatley Quarry lines (either side of Frome) are projected to achieve high - level growth to 2015 (Page 8 , Figure 11 of the link below.)
http://www.networkrail.co.uk/documents/3110_Route%2012%20Reading%20to%20Penzance.pdf

This is due to a projected massive demand for materials during the construction phase of the London 2012 Olympics , which is likely to require a big increase in the number of freight trains from both quarries.

These freight trains , which will be considered essential , will in turn require train paths.

(Post edited to remove defunct link)

Here are some quotes from the November 2004 Guardian article :

"Tomorrow the Department of Transport will publish its community rail development strategy."

"This promises a blueprint to save nearly 60 of the most under-used services in Britain. But other transport initiatives have prompted fears of a clear-out of under-performing services."

"Rail experts say the axing of Britain's worst-performing services is long overdue. Subsidies for all rail services have ballooned to more than £4bn a year. Could it even be time, some whisper, to launch a Beeching II cutback - a second phase of the rail line culling named after Dr Richard Beeching who, as British Railways Board chairman in the 1960s, oversaw the closure of 2,000 little-used stations and the tearing up of hundreds of branch lines."

"But at the same time, the Office of the Rail Regulator has revealed it is carrying out a massive exercise in pinpointing the cost of running many of these lines to 'assess the impact on infrastructure costs of changes in service patterns'."

"Last autumn the SRA's Wider Case for Rail strategy, admitted what government advisers had privately been saying for some time: 'Rail is best when it provides fast, long distance passenger services ... commuter services on busy corridors ... services to major airports [and] rail freight services for regular high volume flows.' It did not list rural services."

"Some rail leaders now privately admit that buses, shared taxis or other modes are sometimes as good as rail - a view confirmed by the success of some operators' own bus services and the choice of buses over tube trains by some London commuters."

"Penistone and six other lines will be named tomorrow as trials for the community rail strategy - which will continue marketing and reduce costs by, for example, adopting 'more appropriate' lower maintenance standards."

A list of Community Rail lines can be found in the link below.
http://www.gnn.gov.uk/environment/fullDetail.asp?ReleaseID=213995&NewsAreaID=2&NavigatedFromDepartment=False

They are ALL on the "least-used lines in Britain" list.

Here is the summary of the original Beeching Report (link below.)
http://www.shropshiretransport.info/beeching/report1/09%20SUMMARY%20OF%20THE%20REPORT.pdf

Here is a link that explains the calculation used by Beeching.
http://www.shropshiretransport.info/beeching/report1/15%20Appendix%202.pdf

The link above also contains the services that he proposed for withdrawal or modification and lists the stations that were to close as a result (not all of them did , and some , like Melksham , closed and then re-opened at a later date.)

Here is a link to the JSPTU Rail Vision. Click on this and read through it.
http://www.jsptu-avon.gov.uk/publications/documents/railstrategy.pdf

Then click on the link below.
http://www.savethetrain.org.uk/forum/index.php?topic=421.msg1243#msg1243

(Post edited to add updated links.)