0844 numbers are certainly not a "reduced" rate.
They are revenue share numbers with two parts to the call price:
1. the revenue share part which costs up to 5 p per minute; this money is passed on from your phone company to the other phone company. Whether they then pass it on to the company you called or just keep it as extra profit is unknown, and somewhat irrelevent - you've already paid it. The revenue share part of the call price is listed here:
http://www.ofcom.org.uk/static/numbering/s8_code.txt and the revenue share depends on the number called.
2. the profit that your phone company adds to the call price; especially noting that if you call from a BT line this is zero pence per minute - BT is currently regulated to not add anything to the price. Other landline operators may add several pence per minute or more to the price. Mobile operators may add 20 to 40 p per minute above the regulated revenue share amount.
0844 numbers are different to 0845 numbers.
0845 numbers used to be "local rate" until 2005. Since 2005 they are just "revenue share" numbers because "local rate" no longer exists (landline operators charge nothing for calls to 01 and 02 numbers of up to one hour duration, and even where the call is chargeable there's just one rate for all calls to 01 and 02 numbers, with NO price difference based on distance). BT has offered 0845 calls as inclusive since 2009. BT subsidise the 2p/min revenue share for 0845 numbers.
0844 numbers are NEVER inclusive.
Rules for 0870 and 0845 numbers will be changing in the next few months to align with those for 0844 and 0871 numbers. 0870 and 0845 will no longer be inclusive.
The Consumer Rights Directive will force "customer service" lines to move from 084 and 087 numbers to 034 and 037 numbers. Those types of calls will then be usable within inclusive minutes from both landlines and mobiles.
Where a company continues using 084 and 087 numbers, the new rules for "unbundled tariffs" will force them to declare the revenue share premium that is built into the call price.
It is already an offence to refer to 0844 and 0845 numbers as "local rate" or "lo-call" rate. 0844 numbers were NEVER any of those things. 0845 were equivalent to "local rate" until 2005, and simply "revenue share" after that ("local rate" ceased to exist in 2005).
See also:
http://en.wikipedia.org/wiki/Non-geographic_telephone_numbers_in_the_United_Kingdom#History_of_non-geographic_prefixes