Can a surety claim against the principal debtor in a personal injury case?

In Bateson v. Gosling (1871), L.R. 7 C.P. 9 at p. 14, Willes J. was of the opinion that ... where the principal [debtor] has entered into a deed of arrangement containing a release subject to the reservation of the creditor's right of recourse against the surety, the latter has no right to raise the objection. Quoting [at p. 15] from Page Wood V.-C. in Webb v. Hewitt (1857), 3 K. & J. 438 at p. 442, 69 E.R. 1181, he said: ... when the right is reserved, the principal debtor cannot say it is inconsistent with giving him time that the creditor should be at liberty to proceed against the sureties, and that they should turn round upon the principal debtor, notwithstanding the time so given him; for, he was a party to the agreement by which that right was reserved to the creditor...

And in Price v. Barker (1855), 4 E1. & B1. 760, 119 E.R. 281, Coleridge J. for the court, at pp. 779-80, said that: ... a covenant not to sue, qualified by a reserve of the remedies against sureties, is to allow the surety to retain all his remedies over against the principal debtor; and that the covenant not to sue is to operate only so far as the rights of the surety may not be affected.