Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

British American Tobacco p.l.c.:

We consent to the incorporation by reference into the Registration Statements (File No. 333-219440 and 333-223678) on Form S-8 of British American Tobacco p.l.c. of our report, dated February 21, 2018, except as described in Note 1.1, as to which the date is October 2, 2018, with respect to the Group Balance Sheet of British American Tobacco p.l.c. and its subsidiaries (the “Group”) as of December 31, 2017 and 2016, the related Group Income Statement, Group Statement of Comprehensive Income, Group Statement of Changes in Equity, and Group Cash Flow Statement for each of the years in the three-year period ended December 31, 2017, and the related notes (collectively, the Group’s “consolidated financial statements”), which report appears in this Report on Form 6-K of British American Tobacco p.l.c. dated October 2, 2018. The audit report refers to a change in the method of accounting for revenue from customers in 2017, 2016, and 2015 due to the adoption of IFRS 15, Revenue from Contracts with Customers. The audit report also refers to a change in the basis of segmentation, which was applied retrospectively to all periods presented.

/s/ KPMG LLP

London, United Kingdom

October 2, 2018