British *rc

In WCB, a British resonant + stop always becomes resonant + fricative as part of a systematic sound-change (cf. Br. *marcos 'horse' > W. march, C. margh, B. marc'h)*.  It has been suggested that Cumbric diverged from this pattern and that the cluster *rc /rk/ remained intact.  The evidence largely comes from examples of Br *landercā 'clearing' (W. llannerch, C. lannergh 'glade'):

• Lanark - Lannarc, Lannerc 12th century
• Barlanark (Glasgow) - no early forms
• Lanercost (Cumbria) - Lanrecost 12th century
• Carlenrig (near Hawick) - Carlanerik 17th century
• Drumlanrig (near Hawick) - Drumlanerk 17th century

Also possibly Lanrekaythin, a lost Cumbria place name, which Jackson describes as 'uncertain'.  These all seem to suggest Br. *rc > Cu. *rc. 

In opposition to this evidence may be cited Lanerch 'Lanark' (15th century) and Lanrechathin 'Lanrekaythin'.  There are several place names containing the equivalent of the personal name W. Meirchion < Br. Marcjānos:  Maughanby (Merghanby, 13th century), Merchiston (Merchinstoun, 13th century) and Powmaughan (Polmergham, 15th century).  There can be little doubt that these originally had /rx/ since the first is now pronounced 'maffenby' (/f/ being a regular English reflex of OE /x/, cf. laugh < hlæhhan), whilst the second retains /rx/ to this day.  To this we might add mercheta, from Leges inter Brettos et Scottos, if it is related to W. merch 'daughter' (which is not certain) and Rederech (W. Rhydderch) from Jocelin's Life of St Kentigern. 

From this evidence, the safest conclusion seems to be that Cumbric regularly had *rch from Br. *rc: all the evidence for Cu. **rc is from a single word and some of the examples are late.  Jackson (1953) suggests that "the development [of Br. *rc > rch] may have been somewhat later in Cumbric" than elsewhere, where he says it occurred in the mid- to late-6th century.  It is noteable that Maughanby and Merchiston both contain later, non-Cumbric elements and have /rx/, whilst the potentially early loans (especially Lanercost) have /rk/ - but to pin a date on any of these names would be hopelessly ad hoc.

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* except for -lt- which is treated differently in each language, never becoming *lth in any case.