Bedfordshire & Luton Archives & Records Service does not hold very many records for Roman Catholic churches and institutions. The reason for this is two fold. Firstly, there are not a large number of Catholic churches in the county, where Protestant nonconformity was always strong. Secondly, Roman Catholic parish archives are sent to the Roman Catholic Diocesan Archive which, for Bedfordshire, is in Northampton.
Thus, the only record Bedfordshire & Luton Archives & Records Service has of Sacred Heart Roman Catholic church in Beaudesert concerns plans to construct a church hall and modernise the Presbytery at 5 Beaudesert between 1966 and 1970 by Leighton Buzzard architects H.A.Rolls and Partners [Z889/2/30].
Fortunately there is a page devoted to the Catholic church in Leighton Buzzard Past and Present, published in 1905:"The founding of the present Leighton Buzzard Catholic Mission on a definite and permanent basis may be said to have commenced in the year 1894. Prior to that period Mass was said occasionally by a visiting priest, either in Leighton or in one or other of the neighbouring villages. For instance, the present Priest of the Leighton mission, Very Rev. Canon Stokes, who was at that time priest of the Wolverton Mission, celebrated Mass at Linslade as long ago as the year 1881; and the late Father Wrigglesworth offered the Holy sacrifice at Hockliffe Grange, when it was in Catholic occupancy. In 1894, premises were rented in North Street, and Father Parkes, who was then the priest of the Wolverton Catholic Church, has also temporary charge of the rising Leighton Mission. For the latter, it was then a day of small things, but even at that period there was much to encourage local Catholics, as is shown by the fact that on the feast of Saint Augustine, the Apostle of England, 1895, a notable event occurred, the Right Rev. Dr. Riddell, Bishop of Northampton, visiting Leighton Buzzard, and administering the Sacrament of Confirmation to a number of candidates, including some adult converts. Special historic interest attached to the incident from the interesting fact that it was the first Confirmation Service for three hundred years held in Leighton Buzzard by a Bishop of the Catholic Church. In the course of the year 1895, the Leighton Mission was provided with a Resident Priest in the person of Rev. Charles E. Reilly, by whose efforts funds were collected with which lands were purchased in Beaudesert, on which a Church and Presbytery were erected. Albeit a small and temporary structure, the interior of the Church is tasteful and devotional, with its gleaming High Altar, its "lamp of fire before the Throne", its pretty shrines, and its Rood Screen of singular pathos and beauty. The Priest of the Mission is the Very Rev. Canon Stokes. The Sunday Services are - Holy Mass, 10.30; Sunday School, 3; Evening Service and benediction of the Blessed Sacrament, 6; Week-day Mass, 8.15".
The Bedfordshire Times of 16th January 1892 adds to the story above. It reported: "ROMAN CATHOLIC MISSION. - For the first time for over 300 years, Holy Mass has just been offered here, in a small room procured by a lady convert. Father Parkes, of Wolverton, intends to say Mass once a month, until the Bishop can inaugurate further arrangements. The Rev. Father Stevenson, a Jesuit priest, and former vicar here, is greatly interested in the movement, and the Pope has sent his special blessing. Much violent opposition has been offered".
The contact details at the time of writing  for anyone wishing to research the history of this church are as follows:
Information Manager & Webmaster
Diocese of Northampton
c/o Ker Anna Centre
Bucks HP27 0JW
Tel. 01844 273337
As Brin is fifty seven miles from the location of the archive in Northampton he may take a while to answer queries or arrange access.