Extracted from Halsbury's Laws of England,
Fourth Edition 39(2) paragraph 524 –

Searches at a registrar’s office.
Every registrar ¹ must, at any time when his office is required to be open for the transaction of public business, ² allow searches to be made in any register of live births or deaths and register of marriages in his keeping and must on payment of the proper fee ³ give a certified copy under his hand of any entry in them ⁴. The right of the public to search the registers of births and deaths cannot be taken away by the Registrar General under his power to make regulations ⁵.
 

1 For the meaning of ‘registrar’ see para 505 note 4 ante; and as to persons required to register marriages see para 558 post.

2 Searches under the Marriage Act 1949 s 63 must be allowed at all reasonable hours: s 63(1). What is a reasonable hour is a question of fact, which must depend on the circumstances of a particular case: see eg Small v Bickley (1875) 32 LT 726.

3 No fee is payable for searches in registers of births, deaths and marriages kept under the Marriage Act 1949 and the Births and Deaths Registration Act 1953, the power to charge such a fee having been repealed by the Registration of Births, Deaths and Marriages (Fees) Order 1968, SI 1968/1242, art 4(1), Sch 2. For the prescribed fees, as 1 April 1998, for (1) a certificated copy of an entry issued under the Marriage Act 1949 s 63(1) (a) when application is made at the time of registering or to a registrar and (b) in other cases; and (2) a certified copy of an entry in registers kept by registrars, see the Registration of Births, Deaths, and Marriages (Fees) Order 1997, SI 1997/2939, art 2, Schedule. There is no fee for a short certificate of birth obtained at the time of registration, or if more than one is obtained, the first of them. For the prescribed fee, as at 1 April 1998, for any other short certificate of birth obtained from a registrar see art 2, Schedule. As to short certificates of birth see para 525 post.

4 See Marriage Act 1949 s 63(1), (2); and the Births and Deaths registration Act 1953 s 32 (both amended by the Registration of Births, Deaths and Marriages (Fees) Order 1968, SI 1968/1242, art 4(1) Sch 2; and the Registration of Births, Deaths and Marriages (Fees) Order 1997, SI 1997/2939, Schedule 1 See also, in relation to the registers of baptisms and burials, the Parochial Registers and Records Measure 1978 s 20(1); the Ecclesiastical Fees Measure 1986 s 2; the Parochial Fees Order 1997, SI 1997/1891, art 1, 2, Schedule ; and ECCESIASTICAL LAW; HUSBAND AND WIFE. Searches in and copies from the register of stillbirths are not allowed except where the registrar with the consent of the Registrar General in any particular case allows: Births and Deaths Registration Act 1953 s 32 proviso. As to short certificates of live births see para 525 post. For the meaning of ‘stillbirth’ see para 504 note 5 ante.

5 Best v Best and McKinley [1920] P 75. There is authority for saying that the right to search includes the right to make extracts as distinct from the right to obtain certified copies on payment of the appropriate fee: see Steele v Williams (1853) 8 Exch 625; but see Re Balaghât Gold Mining Co [1901] 2 KB 665, CA.

Halsbury's Laws of England, paragraph 505 note 4

4  Registration of Births and Deaths Regulations 1987, SI1987/2088, regs 2(2)(b), 7(1), 9(1), (2), Sch 2. Form 1, space 1 (Form 1 substituted by SI 1994/1948). If more than one living child is born at the confinement the registrar must after the date of birth enter the time of birth: Registration of Births and Deaths Regulations 1987, SI 1987/2088, reg 9(2). ‘Registrar’, in relation to any birth or death. means the registrar of births and deaths for the sub-district in which the birth or death takes place, or where any stillborn child is found exposed or any dead body is found and no information as to the place of birth or death is available, for the sub-district in which the child or dead body is found: Births and Deaths Registration Act 1953 s 41 (definition amended by the Children Act 1975 s 108(1)(a). Sch 3 para 13 (1) and see the Interpretation Act 1978 s 11 - As to the registration service see para 605 et seq post.